Dynamical symmetry breaking in asymptotically free field theories

Gross, David J.; Neveu, A.

doi:10.1103/physrevd.10.3235

Cited by 1,835 publications

(2,386 citation statements)

References 29 publications

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“…Solitary waves in the 1+1 dimensional nonlinear Dirac equation have been studied [14,15] in the past in case the nonlinearity parameter k = 1, i.e. the massive Gross-Neveu [16] (with N = 1, i.e. just one localized fermion) and the massive Thirring [17] models.…”

Section: Introductionmentioning

confidence: 99%

Approximate analytic solutions to coupled nonlinear Dirac equations

2017

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We consider the coupled nonlinear Dirac equations (NLDE's) in 1+1 dimensions with scalarscalar self interactions g 2 1 2 (ψψ) 2 + g 2 2 2 (φφ) 2 + g 2 3 (ψψ)(φφ) as well as vector-vector interactions of the form g 2 1 2 (ψγµψ)(ψγ µ ψ) + g 2 2 2 (φγµφ)(φγ µ φ) + g 2 3 (ψγµψ)(φγ µ φ). Writing the two components of the assumed solitary wave solution of these equation in the form ψ = e −iω 1 t {R1 cos θ, R1 sin θ}, φ = e −iω 2 t {R2 cos η, R2 sin η}, and assuming that θ(x), η(x) have the same functional form they had when g3=0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g 2 3 /g 2 2 and g 2 3 /g 2 1 . In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.

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Section: Introductionmentioning

confidence: 99%

Approximate analytic solutions to coupled nonlinear Dirac equations

2017

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“…The focus of our study is to compare the static and dynamical critical phenomena near the critical point obtained from the effective field theory of scalar and pseudoscalar mesons (pions) after integrating out the quarks, and the O(4) linear sigma model which has been argued to describe the universality class for two-flavor QCD [1,2]. The Ginzburg-Landau (GL) description of the linear sigma model (LSM) near the critical point is based on the Lagrangian density [1,2,16] 6) where the coefficients A, B > 0 are non-universal and vary slowly near T c . The T 2 term emerges from the one-loop tadpole contribution to the self-energies which is the leading term at high temperatures and is local [24,25].…”

Section: The Nambu-jona-lasinio Model and The Linear Sigma Modelmentioning

confidence: 99%

“…However, due to the rich nonperturbative structure of QCD current theoretical investigations are limited only to models that incorporate the relevant symmetries and low-energy effective field theories of QCD. Some popular models of chiral dynamics are the linear sigma model [5], the Gross-Neveu model [6], and the Nambu-Jona-Lasinio model [7]. The thermodynamic equilibrium aspects of these models at finite temperature and/or quark chemical potential have been studied extensively in the literature [8,9,10,11], in particular lattice gauge theory has provided an impressive body of results on the phase diagram for temperature and chemical potential (see for example [12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium pion dynamics near the critical point in a constituent quark model

Boyanovsky¹,

Vega²,

Wang³

2004

Nuclear Physics A

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We study static and dynamical critical phenomena of chiral symmetry breaking in a two-flavor Nambu-Jona-Lasinio constituent quark model. We obtain the low-energy effective action for scalar and pseudoscalar degrees of freedom to lowest order in quark loops and to quadratic order in the meson fluctuations around the mean field. The static limit of critical phenomena is shown to be described by a Ginzburg-Landau effective action including spatial gradients. Hence static critical phenomena is described by the universality class of the O(4) Heisenberg ferromagnet. Dynamical critical phenomena is studied by obtaining the equations of motion for pion fluctuations. We find that for T < Tc the are stable long-wavelength pion excitations with dispersion relation ωπ(k) = k described by isolated pion poles. The residue of the pion pole vanishes near Tc as Z ∝ 1/| ln(1 − T /Tc)| and long-wavelength fluctuations are damped out by Landau damping on a time scale t rel (k) ∝ 1/k, reflecting critical slowing down of pion fluctuations near the critical point. At the critical point, the pion propagator features mass shell logarithmic divergences which we conjecture to be the harbinger of a (large) dynamical anomalous dimension. We find that while the classical spinodal line coincides with that of the Ginzburg-Landau theory, the growth rate of long-wavelength spinodal fluctuations has a richer wavelength dependence as a consequence of Landau damping. We argue that Landau damping prevents a local low energy effective action in terms of a derivative expansion in real time at least at the order studied.

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“…Compactification of spatial dimensions [5,6] is considered in a similar way. An unified treatment, generalizing various approaches dealing with finite-temperature and spatialcompactification concurrently, has been constructed [7,8,9] These methods have been employed to investigate spontaneous symmetrybreaking induced by temperature and/or spatial constraints in some bosonic and fermionic models describing phase transitions in condensed-matter, statistical and particle physics; for instance, for describing the size-dependence of the transition temperature of superconducting films, wires and grains [10,11]; for investigating size-effects in first-and second-order transitions [12,13,14,15]; and for analyzing size and magnetic-field effects on the Gross-Neveu (GN) [16] and the Nambu-Jona-Lasinio (NJL) [17] models, taken as effective theories [18] for hadronic physics [19,20,21].…”

Section: Introductionmentioning

confidence: 99%