scholarly journals GAUGE DEPENDENCE AMBIGUITY AND CHEMICAL POTENTIAL IN THERMAL U(1) THEORY

2007 ◽  
Vol 22 (36) ◽  
pp. 2763-2773
Author(s):  
M. LOEWE ◽  
S. MENDIZABAL ◽  
R. A. SANTOS
Keyword(s):  
Phase Transition ◽  
Mass Spectrum ◽  
Effective Potential ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Gauge Dependence ◽  
Dependence Problem ◽  
Gauge Fixing ◽  
The One

In this paper we explore the dependence on the gauge-fixing condition of several quantities in the U(1) Higgs model at finite temperature and chemical potential. We compute the effective potential at the one-loop level, using a gauge-fixing condition that depends on μ and which allows to decouple the contributions of the different fields in the model. In this way we get the mass spectrum and the characterization of the phase transition, pointing out in each case how these quantities depend on the gauge-fixing parameter ξ. When μ vanishes, we agree with previous results if ξ=0. The gauge dependence problem is also analyzed from the perspective of the Nielsen identities.

Ring-diagram summations in the finite-temperature effective potential

1993 ◽  
Vol 71 (5-6) ◽  
pp. 227-236 ◽  
Author(s):  
M. E. Carrington
Keyword(s):  
Phase Transition ◽  
Standard Model ◽  
Effective Potential ◽  
Finite Temperature ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Ring Diagram ◽  
First Order Phase Transition ◽  
The Standard Model ◽  
The One

There has been much recent interest in the finite-temperature effective potential of the standard model in the context of the electroweak phase transition. We review the calculation of the effective potential with particular emphasis on the validity of the expansions that are used. The presence of a term that is cubic in the Higgs condensate in the one-loop effective potential appears to indicate a first-order electroweak phase transition. However, in the high-temperature regime, the infrared singularities inherent in massless models produce cubic terms that are of the same order in the coupling. In this paper, we discuss the inclusion of an infinite set of these terms via the ring-diagram summation, and show that the standard model has a first-order phase transition in the weak coupling expansion.

scholarly journals $$A_0$$-condensation in quark-gluon plasma with finite baryon density

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
M. Bordag ◽  
V. Skalozub
Keyword(s):  
Effective Potential ◽  
Quark Gluon Plasma ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Background Field ◽  
Gluon Plasma ◽  
Baryon Density ◽  
Spontaneous Generation ◽  
Gauge Fixing ◽  
Thermodynamic Pressure

AbstractIn the present paper, we return to the problem of spontaneous generation of the $$A_0$$ A 0 -background field in QCD at finite temperature and a quark chemical potential, $$\mu $$ μ . On the lattice, this problem was studied by different approaches where an analytic continuation to the imaginary potential $$i \mu $$ i μ has been used. Here we consider both, real and imaginary chemical potential, analytically within the two-loop gauge-fixing independent effective potential $$W_{eff.}$$ W e f f . . We realize the gauge independence in to ways: (1) on the base of Nielsen’s identity and (2) expressing the potential in terms of Polyakov’s loop. Firstly we reproduce the known expressions in terms of Bernoulli’s polynomials for the gluons and quarks. Then, we calculate the $$\mu $$ μ -dependence, either for small $$\mu $$ μ as expansion or numerically for finite $$\mu $$ μ , real and imaginary. One result is that the chemical potential only weakly changes the values of the condensate fields, but quite strongly deepens the minima of the effective potential. We investigate the dependence of Polyakov’s loop in the minimum of the effective potential, thermodynamic pressure and Debye’s mass on the chemical potential. Comparisons with other results are given.

scholarly journals A critical look at the electroweak phase transition

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Andreas Ekstedt ◽  
Johan Löfgren
Keyword(s):  
Phase Transition ◽  
Generic Model ◽  
Electroweak Symmetry ◽  
Electroweak Phase Transition ◽  
Gauge Dependence ◽  
Perturbative Methods ◽  
The Standard Model ◽  
Gauge Fixing ◽  
Infrared Divergences ◽  
General Gauge

Abstract The electroweak phase transition broke the electroweak symmetry. Perturbative methods used to calculate observables related to this phase transition suffer from severe problems such as gauge dependence, infrared divergences, and a breakdown of perturbation theory. In this paper we develop robust perturbative tools for dealing with phase transitions. We argue that gauge and infrared problems are absent in a consistent power-counting. We calculate the finite temperature effective potential to two loops for general gauge-fixing parameters in a generic model. We demonstrate gauge invariance, and perform numerical calculations for the Standard Model in Fermi gauge.

scholarly journals EFFECT OF A LOCALLY REPULSIVE INTERACTION ON s-WAVE SUPERCONDUCTORS

2010 ◽  
Vol 22 (03) ◽  
pp. 233-303 ◽  
Author(s):  
J.-B BRU ◽  
W. DE SIQUEIRA PEDRA
Keyword(s):  
Phase Transition ◽  
Chemical Potential ◽  
Large Deviation ◽  
Coulomb Repulsion ◽  
Meissner Effect ◽  
Repulsive Interaction ◽  
S Wave ◽  
Insulator Phase Transition ◽  
The One ◽  
Strong Repulsion

The thermodynamic impact of the Coulomb repulsion on s-wave superconductors is analyzed via a rigorous study of equilibrium and ground states of the strong coupling BCS-Hubbard Hamiltonian. We show that the one-site electron repulsion can favor superconductivity at fixed chemical potential by increasing the critical temperature and/or the Cooper pair condensate density. If the one-site repulsion is not too large, a first or a second order superconducting phase transition can appear at low temperatures. The Meißner effect is shown to be rather generic but coexistence of superconducting and ferromagnetic phases is also shown to be feasible, for instance, near half-filling and at strong repulsion. Our proof of a superconductor-Mott insulator phase transition implies a rigorous explanation of the necessity of doping insulators to create superconductors. These mathematical results are consequences of "quantum large deviation" arguments combined with an adaptation of the proof of Størmer's theorem [1] to even states on the CAR algebra.

Studies on proper time regularization and the QCD chiral phase transition

2019 ◽  
Vol 34 (01) ◽  
pp. 1950003
Author(s):  
Yu-Qiang Cui ◽  
Zhong-Liang Pan
Keyword(s):  
Phase Transition ◽  
Small Parameter ◽  
Effective Mass ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Proper Time ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Njl Model ◽  
The Difference

We investigate the finite-temperature and zero quark chemical potential QCD chiral phase transition of strongly interacting matter within the two-flavor Nambu–Jona-Lasinio (NJL) model as well as the proper time regularization. We use two different regularization processes, as discussed in Refs. 36 and 37, separately, to discuss how the effective mass M varies with the temperature T. Based on the calculation, we find that the M of both regularization schemes decreases when T increases. However, for three different parameter sets, quite different behaviors will show up. The results obtained by the method in Ref. 36 are very close to each other, but those in Ref. 37 are getting farther and farther from each other. This means that although the method in Ref. 37 seems physically more reasonable, it loses the advantage in Ref. 36 of a small parameter dependence. In addition, we also, find that two regularization schemes provide similar results when T [Formula: see text] 100 MeV, while when T is larger than 100 MeV, the difference becomes obvious: the M calculated by the method in Ref. 36 decreases more rapidly than that in Ref. 37.

PHASE TRANSITIONS IN THE ABELIAN HIGGS MODEL AT FINITE DENSITIES

1991 ◽  
Vol 06 (23) ◽  
pp. 4063-4076 ◽  
Author(s):  
V.J. PETER ◽  
M. SABIR
Keyword(s):  
Phase Transitions ◽  
Density Dependence ◽  
Gauge Invariance ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Higgs Model ◽  
Coupling Constants ◽  
Abelian Higgs Model ◽  
Multiple Phase ◽  
The One

We study the U(1)-invariant Abelian Higgs model at a finite temperature and a finite chemical potential, at the one-loop level of approximation, and show the existence of chemical-potential-induced multiple-phase transitions at finite temperatures. The temperature and density dependence of the coupling constants is also analyzed. The gauge invariance of the results obtained is demonstrated.

scholarly journals REFINEMENTS IN EFFECTIVE POTENTIAL CALCULATIONS IN THE MSSM

2006 ◽  
Vol 21 (40) ◽  
pp. 3009-3020
Author(s):  
M. ARGYROU ◽  
A. KATSIKATSOU ◽  
I. MALAMOS
Keyword(s):  
Effective Potential ◽  
Dominant Role ◽  
Higgs Sector ◽  
Electroweak Symmetry Breaking ◽  
Electroweak Symmetry ◽  
Gauge Dependence ◽  
Precise Calculation ◽  
Mixing Parameter ◽  
The One ◽  
Supersymmetric Theories

The one-loop effective potential is a powerful tool in studying the electroweak symmetry breaking of supersymmetric theories, whose precise calculation may have important phenomenological consequences. In this work, we are correctly treating the contribution of the Higgs sector to the effective potential and refine the radiative corrections to the Higgs mixing parameter μ, which is known to affect greatly the supersymmetric spectrum. Working at the average stop scale to minimize the effect of the stop sector, we find additional corrections which can play a dominant role in the focus point region of the parameter space of the MSSM. The comparison of our results with those of the literature is discussed. We also discuss the gauge dependence of the effective potential and its effect on the μ parameter in analyses where this is determined from the one-loop minimization conditions of the effective potential.

FINITE TEMPERATURE EFFECTIVE POTENTIAL IN A KALUZA-KLEIN UNIVERSE

1990 ◽  
Vol 05 (02) ◽  
pp. 353-361 ◽  
Author(s):  
PINAKI ROY
Keyword(s):  
Low Temperature ◽  
Effective Potential ◽  
Finite Temperature ◽  
Scalar Fields ◽  
Walker Metric ◽  
The One ◽  
Kaluza Klein

We evaluate the finite temperature one-loop effective potential for scalar fields in Kaluza-Klein universe consisting of the product of a space with open Robertson-Walker metric and the N sphere SN. The one-loop effective potential has been computed in both high and low temperature limits.

The two-flavor NJL model with two-cutoff proper time regularization

2014 ◽  
Vol 29 ◽  
pp. 1460232 ◽  
Author(s):  
Zhu-Fang Cui ◽  
Yi-Lun Du ◽  
Hong-Shi Zong
Keyword(s):  
Phase Transition ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Proper Time ◽  
Model Parameters ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Regularization Scheme ◽  
Njl Model

In this paper, we use the two-flavor Nambu–Jona-Lasinio model together with the proper time regularization that has both ultraviolet and infrared cutoffs to study the chiral phase transition at finite temperature and zero chemical potential. The involved model parameters in our calculation are determined in the traditional way. Our calculations show that the dependence of the results on the choice of the parameters are really small, which can then be regarded as an advantage besides such a regularization scheme is Lorentz invariant.

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