QCD vacuum

The Quantum Chromodynamic Vacuum or QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks. The presence of these condensates characterizes the confined phase of quark matter.

Question, Web Fundamentals.svg Unsolved problem in physics:
QCD in the non-perturbative regime: confinement. The equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei. How does QCD give rise to the physics of nuclei and nuclear constituents?
(more unsolved problems in physics)

Symmetries and symmetry breaking

Symmetries of the QCD Lagrangian

Like any relativistic quantum field theory, QCD enjoys Poincaré symmetry including the discrete symmetries CPT (each of which is realized). Apart from these space-time symmetries, it also has internal symmetries. Since QCD is an SU(3) gauge theory, it has local SU(3) gauge symmetry.

Since it has many flavours of quarks, it has approximate flavour and chiral symmetry. This approximation is said to involve the chiral limit of QCD. Of these chiral symmetries, the baryon number symmetry is exact. Some of the broken symmetries include the axial U(1) symmetry of the flavour group. This is broken by the chiral anomaly. The presence of instantons implied by this anomaly also breaks CP symmetry.

In summary, the QCD Lagrangian has the following symmetries:

The following classical symmetries are broken in the QCD Lagrangian:

Spontaneous symmetry breaking

When the Hamiltonian of a system (or the Lagrangian) has a certain symmetry, but the vacuum does not, then one says that spontaneous symmetry breaking (SSB) has taken place.

A familiar example of SSB is in ferromagnetic materials. Microscopically, the material consists of atoms with a non-vanishing spin, each of which acts like a tiny bar magnet, i.e., a magnetic dipole. The Hamiltonian of the material, describing the interaction of neighbouring dipoles, is invariant under rotations. At high temperature, there is no magnetization of a large sample of the material. Then one says that the symmetry of the Hamiltonian is realized by the system. However, at low temperature, there could be an overall magnetization. This magnetization has a preferred direction, since one can tell the north magnetic pole of the sample from the south magnetic pole. In this case, there is spontaneous symmetry breaking of the rotational symmetry of the Hamiltonian.

When a continuous symmetry is spontaneously broken, massless bosons appear, corresponding to the remaining symmetry. This is called the Goldstone phenomenon and the bosons are called Goldstone bosons.

Symmetries of the QCD vacuum

The SU(Nf) × SU(Nf) chiral flavour symmetry of the QCD Lagrangian is broken in the vacuum state of the theory. The symmetry of the vacuum state is the diagonal SU(Nf) part of the chiral group. The diagnostic for this is the formation of a non-vanishing chiral condensate ψiψi, where ψi is the quark field operator, and the flavour index i is summed. The Goldstone bosons of the symmetry breaking are the pseudoscalar mesons.

When Nf=2, i.e., only the up and down quarks are treated as massless, the three pions are the Goldstone bosons. When the strange quark is also treated as massless, i.e., Nf = 3, all eight pseudoscalar mesons of the quark model become Goldstone bosons. The actual masses of these mesons are obtained in chiral perturbation theory through an expansion in the (small) actual masses of the quarks.

In other phases of quark matter the full chiral flavour symmetry may be recovered, or broken in completely different ways.

Experimental evidence

The evidence for QCD condensates comes from two eras, the pre-QCD era 1950–1973 and the post-QCD era, after 1974. The pre-QCD results established that the strong interactions vacuum contains a quark chiral condensate, while the post-QCD results established that the vacuum also contains a gluon condensate.

Motivating results

Gradient coupling

In the 1950s, there were many attempts to produce a field theory to describe the interactions of pions and nucleons. The obvious renormalizable interaction between the two objects is the Yukawa coupling to a pseudoscalar:

And this is clearly theoretically correct, since it is leading order and it takes all the symmetries into account. But it doesn't match experiment. The interaction that does couples the nucleons to the gradient of the pion field.

This is the gradient-coupling model. This interaction has a very different dependence on the energy of the pion—it vanishes at zero momentum.

This type of coupling means that a coherent state of low momentum pions barely interacts at all. This is a manifestation of an approximate symmetry, a shift symmetry of the pion field. The replacement

leaves the gradient coupling alone, but not the pseudoscalar coupling.

The modern explanation for the shift symmetry was first proposed by Yoichiro Nambu. The pion field is a Goldstone boson, and the shift symmetry is the lowest order approximation to moving along the flat directions.

Goldberger–Treiman relation

There is a mysterious relationship between the strong interaction coupling of the pions to the nucleons, the coefficient g in the gradient coupling model, and the axial vector current coefficient of the nucleon which determines the weak decay rate of the neutron. The relation is

and it is obeyed to 10% accuracy.

The constant GA is the coefficient that determines the neutron decay rate. It gives the normalization of the weak interaction matrix elements for the nucleon. On the other hand, the pion-nucleon coupling is a phenomenological constant describing the scattering of bound states of quarks and gluons.

The weak interactions are current-current interactions ultimately because they come from a non-Abelian gauge theory. The Goldberger–Treiman relation suggests that the pions for some reason interact as if they are related to the same symmetry current.

The phenomenon which gives rise to the Goldberger–Treiman relation was called the partially conserved axial current (PCAC) hypothesis. Partially conserved is an archaic term for spontaneously broken, and the axial current is now called the chiral symmetry current.

The idea is that the symmetry current which performs axial rotations on the fundamental fields does not preserve the vacuum. This means that the current J applied to the vacuum produces particles. The particles must be spinless, otherwise the vacuum wouldn't be Lorentz invariant. By index matching, the matrix element is:

where kμ is the momentum carried by the created pion. Since the divergence of the axial current operator is zero, we must have

Hence the pions are massless, m2
= 0
, in accordance with Goldstone's theorem.

Now if the scattering matrix element is considered, we have

Up to a momentum factor, which is the gradient in the coupling, it takes the same form as the axial current turning a neutron into a proton in the current-current form of the weak interaction.

Soft pion emission

Extensions of the PCAC ideas allowed Steven Weinberg to calculate the amplitudes for collisions which emit low energy pions from the amplitude for the same process with no pions. The amplitudes are those given by acting with symmetry currents on the external particles of the collision.

These successes established the basic properties of the strong interaction vacuum well before QCD.

Pseudo-Goldstone bosons

Experimentally it is seen that the masses of the octet of pseudoscalar mesons is very much lighter than the next lightest states; i.e., the octet of vector mesons (such as the rho meson). The most convincing evidence for SSB of the chiral flavour symmetry of QCD is the appearance of these pseudo-Goldstone bosons. These would have been strictly massless in the chiral limit. There is convincing demonstration that the observed masses are compatible with chiral perturbation theory. The internal consistency of this argument is further checked by lattice QCD computations which allow one to vary the quark mass and check that the variation of the pseudoscalar masses with the quark mass is as required by chiral perturbation theory.

Eta prime meson

This pattern of SSB solves one of the earlier "mysteries" of the quark model, where all the pseudoscalar mesons should have been of nearly the same mass. Since Nf = 3, there should have been nine of these. However, one (the SU(3) singlet η′ meson) has quite a larger mass than the SU(3) octet. In the quark model, this has no natural explanation – a mystery named the η−η′ mass splitting (the η is one member of the octet, which should have been degenerate in mass with the η′).

In QCD, one realizes that the η′ is associated with the axial UA(1) which is explicitly broken through the chiral anomaly, and thus its mass is not "protected" to be small, like that of the η. The η–η′ mass splitting can be explained[1] [2] [3] through the 't Hooft instanton mechanism,[4] whose 1/N realization is also known as Witten–Veneziano mechanism.[5] [6]

Current algebra and QCD sum rules

PCAC and current algebra also provide evidence for this pattern of SSB. Direct estimates of the chiral condensate also come from such analysis.

Another method of analysis of correlation functions in QCD is through an operator product expansion (OPE). This writes the vacuum expectation value of a non-local operator as a sum over VEVs of local operators, i.e., condensates. The value of the correlation function then dictates the values of the condensates. Analysis of many separate correlation functions gives consistent results for several condensates, including the gluon condensate, the quark condensate, and many mixed and higher order condensates. In particular one obtains

Here G refers to the gluon field tensor, ψ to the quark field, and g to the QCD coupling.

These analyses are being refined further through improved sum rule estimates and direct estimates in lattice QCD. They provide the raw data which must be explained by models of the QCD vacuum.

Models of the QCD vacuum

A full solution of QCD should give a full description of the vacuum, confinement and the hadron spectrum. Lattice QCD is making rapid progress towards providing the solution as a systematically improvable numerical computation. However, approximate models of the QCD vacuum remain useful in more restricted domains. The purpose of these models is to make quantitative sense of some set of condensates and hadron properties such as masses and form factors.

This section is devoted to models. Opposed to these are systematically improvable computational procedures such as large N QCD and lattice QCD, which are described in their own articles.

The Savvidy vacuum, instabilities and structure

The Savvidy vacuum is a model of the QCD vacuum which at a basic level is a statement that it cannot be the conventional Fock vacuum empty of particles and fields. In 1977, George Savvidy showed[7] that the QCD vacuum with zero field strength is unstable, and decays into a state with a calculable non vanishing value of the field. Since condensates are scalar, it seems like a good first approximation that the vacuum contains some non-zero but homogeneous field which gives rise to these condensates. However, Stanley Mandelstam showed that a homogeneous vacuum field is also unstable. The instability of a homogeneous gluon field was argued by Niels Kjær Nielsen and Poul Olesen in their 1978 paper.[8] These arguments suggest that the scalar condensates are an effective long-distance description of the vacuum, and at short distances, below the QCD scale, the vacuum may have structure.

The dual superconducting model

In a type II superconductor, electric charges condense into Cooper pairs. As a result, magnetic flux is squeezed into tubes. In the dual superconductor picture of the QCD vacuum, chromomagnetic monopoles condense into dual Cooper pairs, causing chromoelectric flux to be squeezed into tubes. As a result, confinement and the string picture of hadrons follows. This dual superconductor picture is due to Gerard 't Hooft and Stanley Mandelstam. 't Hooft showed further that an Abelian projection of a non-Abelian gauge theory contains magnetic monopoles.

While the vortices in a type II superconductor are neatly arranged into a hexagonal or occasionally square lattice, as is reviewed in Olesen's 1980 seminar[9] one may expect a much more complicated and possibly dynamical structure in QCD. For example, nonabelian Abrikosov-Nielsen-Olesen vortices may vibrate wildly or be knotted.

String models

String models of confinement and hadrons have a long history. They were first invented to explain certain aspects of crossing symmetry in the scattering of two mesons. They were also found to be useful in the description of certain properties of the Regge trajectory of the hadrons. These early developments took on a life of their own called the dual resonance model (later renamed string theory). However, even after the development of QCD string models continued to play a role in the physics of strong interactions. These models are called non-fundamental strings or QCD strings, since they should be derived from QCD, as they are, in certain approximations such as the strong coupling limit of lattice QCD.

The model states that the colour electric flux between a quark and an antiquark collapses into a string, rather than spreading out into a Coulomb field as the normal electric flux does. This string also obeys a different force law. It behaves as if the string had constant tension, so that separating out the ends (quarks) would give a potential energy increasing linearly with the separation. When the energy is higher than that of a meson, the string breaks and the two new ends become a quark-antiquark pair, thus describing the creation of a meson. Thus confinement is incorporated naturally into the model.

In the form of the Lund model Monte Carlo program, this picture has had remarkable success in explaining experimental data collected in electron-electron and hadron-hadron collisions.

Bag models

Strictly, these models are not models of the QCD vacuum, but of physical single particle quantum states — the hadrons. The model proposed originally in 1974 by A. Chodos et al. [10] consists of inserting a quark model in a perturbative vacuum inside a volume of space called a bag. Outside this bag is the real QCD vacuum, whose effect is taken into account through the difference between energy density of the true QCD vacuum and the perturbative vacuum (bag constant B) and boundary conditions imposed on the quark wave functions and the gluon field. The hadron spectrum is obtained by solving the Dirac equation for quarks and the Yang–Mills equations for gluons. The wave functions of the quarks satisfy the boundary conditions of a fermion in an infinitely deep potential well of scalar type with respect to the Lorentz group. The boundary conditions for the gluon field are those of the dual color superconductor. The role of such a superconductor is attributed to the physical vacuum of QCD. Bag models strictly prohibit the existence of open color (free quarks, free gluons, etc.) and lead in particular to string models of hadrons.

The chiral bag model[11][12] couples the axial vector current ψγ5γμψ of the quarks at the bag boundary to a pionic field outside of the bag. In the most common formulation, the chiral bag model basically replaces the interior of the skyrmion with the bag of quarks. Very curiously, most physical properties of the nucleon become mostly insensitive to the bag radius. Prototypically, the baryon number of the chiral bag remains an integer, independent of bag radius: the exterior baryon number is identified with the topological winding number density of the Skyrme soliton, while the interior baryon number consists of the valence quarks (totaling to one) plus the spectral asymmetry of the quark eigenstates in the bag. The spectral asymmetry is just the vacuum expectation value ψγ0ψ summed over all of the quark eigenstates in the bag. Other values, such as the total mass and the axial coupling constant gA, are not precisely invariant like the baryon number, but are mostly insensitive to the bag radius, as long as the bag radius is kept below the nucleon diameter. Because the quarks are treated as free quarks inside the bag, the radius-independence in a sense validates the idea of asymptotic freedom.

Instanton ensemble

Another view states that BPST-like instantons play an important role in the vacuum structure of QCD. These instantons were discovered in 1975 by Alexander Belavin, Alexander Markovich Polyakov, Albert S. Schwarz and Yu. S. Tyupkin[13] as topologically stable solutions to the Yang-Mills field equations. They represent tunneling transitions from one vacuum state to another. These instantons are indeed found in lattice calculations. The first computations performed with instantons used the dilute gas approximation. The results obtained did not solve the infrared problem of QCD, making many physicists turn away from instanton physics. Later, though, an instanton liquid model was proposed, turning out to be more promising an approach.[14]

The dilute instanton gas model departs from the supposition that the QCD vacuum consists of a gas of BPST-like instantons. Although only the solutions with one or few instantons (or anti-instantons) are known exactly, a dilute gas of instantons and anti-instantons can be approximated by considering a superposition of one-instanton solutions at great distances from one another. Gerard 't Hooft calculated the effective action for such an ensemble,[15] and he found an infrared divergence for big instantons, meaning that an infinite amount of infinitely big instantons would populate the vacuum.

Later, an instanton liquid model was studied. This model starts from the assumption that an ensemble of instantons cannot be described by a mere sum of separate instantons. Various models have been proposed, introducing interactions between instantons or using variational methods (like the "valley approximation") endeavoring to approximate the exact multi-instanton solution as closely as possible. Many phenomenological successes have been reached.[14] Whether an instanton liquid can explain confinement in 3+1 dimensional QCD is not known, but many physicists think that it is unlikely.

Center vortex picture

A more recent picture of the QCD vacuum is one in which center vortices play an important role. These vortices are topological defects carrying a center element as charge. These vortices are usually studied using lattice simulations, and it has been found that the behavior of the vortices is closely linked with the confinementdeconfinement phase transition: in the confinement phase vortices percolate and fill the spacetime volume, in the deconfinement phase they are much suppressed.[16] Also it has been shown that the string tension vanished upon removal of center vortices from the simulations,[17] hinting at an important role for center vortices.

See also


  1. ^ Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio (2005). "Topological Susceptibility in SU(3) Gauge Theory" (PDF). Phys. Rev. Lett. 94 (32003): 032003. arXiv:hep-th/0407052. Bibcode:2005PhRvL..94c2003D. doi:10.1103/PhysRevLett.94.032003. PMID 15698253. Retrieved 4 March 2015.
  2. ^ Lüscher, Martin; Palombi, Filippo (September 2010). "Universality of the topological susceptibility in the SU(3) gauge theory". Journal of High Energy Physics (JHEP). 2010 (9): 110. arXiv:1008.0732. Bibcode:2010JHEP...09..110L. doi:10.1007/JHEP09(2010)110.
  3. ^ Cè M, Consonni C, Engel G, Giusti L (30 October 2014). "Testing the Witten–Veneziano mechanism with the Yang–Mills gradient flow on the lattice". v1. arXiv:1410.8358. Bibcode:2014arXiv1410.8358C.
  4. ^ 't Hooft, Gerard (5 July 1976). "Symmetry Breaking through Bell–Jackiw Anomalies". Phys. Rev. Lett. 37 (1): 8–11. Bibcode:1976PhRvL..37....8T. doi:10.1103/PhysRevLett.37.8.
  5. ^ Witten, Edward (17 April 1979). "Current algebra theorems for the U(1) "Goldstone boson"". Nuclear Physics B. 156 (2): 269–283. Bibcode:1979NuPhB.156..269W. doi:10.1016/0550-3213(79)90031-2.
  6. ^ Veneziano, Gabriele (14 May 1979). "U(1) without instantons". Nuclear Physics B. 159 (1–2): 213–224. Bibcode:1979NuPhB.159..213V. doi:10.1016/0550-3213(79)90332-8.
  7. ^ Savvidy, G. K. (1977). "Infrared instability of the vacuum state of gauge theories and asymptotic freedom". Phys. Lett. B. 1 (1): 133–134. Bibcode:1977PhLB...71..133S. doi:10.1016/0370-2693(77)90759-6.
  8. ^ Nielsen, Niels Kjær; Olesen, Poul (1978). "An unstable Yang–Mills field mode". Nucl. Phys. B. 144 (2–3): 376–396. Bibcode:1978NuPhB.144..376N. doi:10.1016/0550-3213(78)90377-2.
  9. ^ Olesen, P. (1981). "On the QCD vacuum". Phys. Scripta. 23 (5B): 1000–1004. Bibcode:1981PhyS...23.1000O. doi:10.1088/0031-8949/23/5B/018.
  10. ^ Chodos, A.; Jaffe, R. L.; Johnson, K.; Thorn, C. B.; Weisskopf, V. F. (1974). "New extended model of hadrons". Phys. Rev. D. 9 (12): 3471–3495. Bibcode:1974PhRvD...9.3471C. doi:10.1103/PhysRevD.9.3471.
  11. ^ Linas Vepstas, A.D. Jackson, "Justifying the Chiral Bag", Physics Reports Volume 187, Issue 3, March 1990, Pages 109-143.
  12. ^ Atsushi Hosaka, Hiroshi Toki, "Chiral bag model for the nucleon", Physics Reports Volume 277, Issues 2–3, December 1996, Pages 65-188.
  13. ^ Belavin, A.A.; Polyakov, A. M.; Schwartz, A. S.; Tyupkin, Yu. S. (1975). "Pseudoparticle solutions of the Yang-Mills equations". Phys. Lett. 59B (1): 85–87. Bibcode:1975PhLB...59...85B. doi:10.1016/0370-2693(75)90163-X.
  14. ^ a b Hutter, Marcus (1995). "Instantons in QCD: Theory and application of the instanton liquid model". arXiv:hep-ph/0107098.
  15. ^ 't Hooft, Gerard (1976). "Computation of the quantum effects due to a four-dimensional pseudoparticle". Phys. Rev. D14 (12): 3432–3450. Bibcode:1976PhRvD..14.3432T. doi:10.1103/PhysRevD.14.3432.
  16. ^ Engelhardt, M.; Langfeld, K.; Reinhardt, H.; Tennert, O. (2000). "Deconfinement in SU(2) Yang–Mills theory as a center vortex percolation transition". Physical Review D. 61 (5): 054504. arXiv:hep-lat/9904004. Bibcode:2000PhRvD..61e4504E. doi:10.1103/PhysRevD.61.054504.
  17. ^ Del Debbio, L.; Faber, M.; Greensite, J.; Olejník, Š. (1997). "Center dominance and Z2 vortices in SU(2) lattice gauge theory". Physical Review D. 55 (4): 2298–2306. arXiv:hep-lat/9610005. Bibcode:1997PhRvD..55.2298D. doi:10.1103/PhysRevD.55.2298.


  • Watson, Andrew (2004-10-07). The Quantum Quark. ISBN 978-0-521-82907-6.
  • Shifman, M. A. Handbook of QCD. ISBN 978-981-238-028-9.
  • Shuryak, E. V. (2004). The QCD Vacuum, Hadrons and Superdense Matter. ISBN 978-981-238-574-1.
Alexander Markovich Polyakov

Alexander Markovich Polyakov (Russian: Алекса́ндр Ма́ркович Поляко́в; born 27 September 1945) is a Russian theoretical physicist, formerly at the Landau Institute in Moscow and, since 1990, at Princeton University.

Chiral symmetry breaking

In particle physics, chiral symmetry breaking is the spontaneous symmetry breaking of a chiral symmetry – usually by a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction. Yoichiro Nambu was awarded the 2008 Nobel prize in physics for describing this phenomenon ("for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics").

Color confinement

In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color charged particles (such as quarks and gluons) cannot be isolated, and therefore cannot be directly observed in normal conditions below the Hagedorn temperature of approximately 2 trillion kelvin (corresponding to energies of approximately 130–140 MeV per particle). Quarks and gluons must clump together to form hadrons. The two main types of hadron are the mesons (one quark, one antiquark) and the baryons (three quarks). In addition, colorless glueballs formed only of gluons are also consistent with confinement, though difficult to identify experimentally. Quarks and gluons cannot be separated from their parent hadron without producing new hadrons.


Condensate may refer to:

The liquid phase produced by the condensation of steam or any other gas

The product of a chemical condensation reaction, other than water

Natural-gas condensate, in the natural gas industry

Condensate (album), a 2011 album by The Original 7ven, the band formerly known as The Time

Dual superconductor model

In the theory of quantum chromodynamics, dual superconductor models attempt to explain confinement of quarks in terms of an electromagnetic dual theory of superconductivity.

Fermionic condensate

A fermionic condensate is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic atoms under similar conditions. The earliest recognized fermionic condensate described the state of electrons in a superconductor; the physics of other examples including recent work with fermionic atoms is analogous. The first atomic fermionic condensate was created by a team led by Deborah S. Jin in 2003.

Fractional quantum mechanics

In physics, fractional quantum mechanics is a generalization of standard quantum mechanics, which naturally comes out when the Brownian-like quantum paths substitute with the Lévy-like ones in the Feynman path integral. This concept was discovered by Nick Laskin who coined the term fractional quantum mechanics.

Gluon condensate

In quantum chromodynamics (QCD), the gluon condensate is a non-perturbative property of the QCD vacuum which could be partly responsible for giving masses to light mesons.

If the gluon field tensor is represented as Gμν, then the gluon condensate is the vacuum expectation value . It is not clear yet whether this condensate is related to any of the known phase changes[which?] in quark matter. There have been scattered studies of other types of gluon condensates, involving a different number of gluon fields.

For more on the context in which this quantity occurs, see the article on the QCD vacuum.

Horror vacui (physics)

In physics, horror vacui, or plenism (), commonly stated as "nature abhors a vacuum", is a postulate attributed to Aristotle, who articulated a belief, later criticized by the atomism of Epicurus and Lucretius, that nature contains no vacuums because the denser surrounding material continuum would immediately fill the rarity of an incipient void. He also argued against the void in a more abstract sense (as "separable"), for example, that by definition a void, itself, is nothing, and following Plato, nothing cannot rightly be said to exist. Furthermore, insofar as it would be featureless, it could neither be encountered by the senses, nor could its supposition lend additional explanatory power. Hero of Alexandria challenged the theory in the first century CE, but his attempts to create an artificial vacuum failed. The theory was debated in the context of 17th-century fluid mechanics, by Thomas Hobbes and Robert Boyle, among others, and through the early 18th century by Sir Isaac Newton and Gottfried Leibniz.

Index of physics articles (Q)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

Johann Rafelski

Johann Rafelski (born 19 May 1950) is a German-American theoretical physicist. He is Professor of Physics at The University of Arizona in Tucson, guest scientist at CERN (Geneva), and has been LMU-Excellent Guest Professor at the Ludwig Maximilian University of Munich in Munich, Germany.

Rafelski's current research interests center around investigation of the vacuum structure of QCD and QED in the presence of strong fields; study of the QCD vacuum structure and deconfinement with strange particle production in deconfined quark–gluon plasma formed in relativistic heavy ion collisions; the formation of matter out of quark-gluon plasma in the hadronization process, also in the early Universe; the ascent of ultrashort laser light pulses as a new tool in this domain of physics. He has also contributed to the physics of table top Muon-catalyzed fusion, antimatter formation and annihilation, and artificial intelligence.

Nuclear matter

Nuclear matter is an idealized system of interacting nucleons (protons and neutrons) that exists in several phases that as yet are not fully established. It is not matter in a nucleus, but a hypothetical substance consisting of a huge number of protons and neutrons interacting by only nuclear forces and no Coulomb forces. Volume and the number of particles are infinite, but the ratio is finite. Infinite volume implies no surface effects and translational invariance (only differences in position matter, not absolute positions).

A common idealization is symmetric nuclear matter, which consists of equal numbers of protons and neutrons, with no electrons.

When nuclear matter is compressed to sufficiently high density, it is expected, on the basis of the asymptotic freedom of Quantum chromodynamics, that it will become quark matter, which is a degenerate Fermi gas of quarks.

Some authors use "nuclear matter" in a broader sense, and refer to the model described above as "infinite nuclear matter", and consider it as a "toy model", a testing ground for analytical techniques. However, the composition of a neutron star, which requires more than neutrons and protons, is not necessarily locally charge neutral, and does not exhibit translation invariance, often is differently referred to, for example, as neutron star matter or stellar matter and is considered distinct from nuclear matter. In a neutron star, pressure rises from zero (at the surface) to an unknown large value in the center.

Methods capable of treating finite regions have been applied to stars and to atomic nuclei. One such model for finite nuclei is the liquid drop model, which includes surface effects and Coulomb interactions.

QCD sum rules

In quantum chromodynamics, the confining and strong coupling nature of the theory means that conventional perturbative techniques often fail to apply. The QCD sum rules (or Shifman–Vainshtein–Zakharov sum rules) are a way of dealing with this. The idea is to work with gauge invariant operators and operator product expansions of them. The vacuum to vacuum correlation function for the product of two such operators can be reexpressed as

where we have inserted hadronic particle states on the right hand side.

QED vacuum

The Quantum Electrodynamic Vacuum or QED vacuum is the field-theoretic vacuum of quantum electrodynamics. It is the lowest energy state (the ground state) of the electromagnetic field when the fields are quantized. When Planck's constant is hypothetically allowed to approach zero, QED vacuum is converted to classical vacuum, which is to say, the vacuum of classical electromagnetism.Another field-theoretic vacuum is the QCD vacuum of the Standard Model.

Quantum calculus

Quantum calculus, sometimes called calculus without limits, is equivalent to traditional infinitesimal calculus without the notion of limits. It defines "q-calculus" and "h-calculus", where h ostensibly stands for Planck's constant while q stands for quantum. The two parameters are related by the formula

where is the reduced Planck constant.

Quantum cosmology

Quantum cosmology is the attempt in theoretical physics to develop a quantum theory of the Universe. This approach attempts to answer open questions of classical physical cosmology, particularly those related to the first phases of the universe.

The classical cosmology is based on Albert Einstein's general theory of relativity (GTR or simply GR). It describes the evolution of the universe very well, as long as you do not approach the Big Bang. It is the gravitational singularity and the Planck time where relativity theory fails to provide what must be demanded of a final theory of space and time. Therefore, a theory is needed that integrates relativity theory and quantum theory. Such an approach is attempted for instance with the loop quantum gravity, the string theory and the causal set theory.

Quantum vacuum (disambiguation)

The quantum vacuum state or simply quantum vacuum refers to the quantum state with the lowest possible energy.

Quantum vacuum may also refer to:

Quantum chromodynamic vacuum (QCD vacuum), a non-perturbative vacuum

Quantum electrodynamic vacuum (QED vacuum), a field-theoretic vacuum

Quantum vacuum (ground state), the state of lowest energy of a quantum system

Quantum vacuum collapse, a hypothetical vacuum metastability event

Quantum vacuum expectation value, an operator's average, expected value in a quantum vacuum

Quantum vacuum energy, an underlying background energy that exists in space throughout the entire Universe

The Quantum Vacuum: An Introduction to Quantum Electrodynamics, physics textbook authored by Peter W. Milonni

Symmetry breaking

In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations (or "noise"), the choice will appear arbitrary. This process is called symmetry "breaking", because such transitions usually bring the system from a symmetric but disorderly state into one or more definite states. Symmetry breaking is thought to play a major role in pattern formation.

In 1972, Nobel laureate P.W. Anderson used the idea of symmetry breaking to show some of the drawbacks of reductionism in his paper titled "More is different" in Science.Symmetry breaking can be distinguished into two types, explicit symmetry breaking and spontaneous symmetry breaking, characterized by whether the equations of motion fail to be invariant or the ground state fails to be invariant.

Vacuum state

In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. Zero-point field is sometimes used as a synonym for the vacuum state of an individual quantized field.

According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space". According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence.The QED vacuum of quantum electrodynamics (or QED) was the first vacuum of quantum field theory to be developed. QED originated in the 1930s, and in the late 1940s and early 1950s it was reformulated by Feynman, Tomonaga and Schwinger, who jointly received the Nobel prize for this work in 1965. Today the electromagnetic interactions and the weak interactions are unified in the theory of the electroweak interaction.

The Standard Model is a generalization of the QED work to include all the known elementary particles and their interactions (except gravity). Quantum chromodynamics is the portion of the Standard Model that deals with strong interactions, and QCD vacuum is the vacuum of quantum chromodynamics. It is the object of study in the Large Hadron Collider and the Relativistic Heavy Ion Collider, and is related to the so-called vacuum structure of strong interactions.

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