scholarly journals Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory

2012 ◽  
Vol 86 (10) ◽  
Author(s):  
K. G. Klimenko ◽  
R. N. Zhokhov ◽  
V. Ch. Zhukovsky
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
Chemical Potential ◽  
Superconducting Phase ◽  
Quantum Field

Understanding Phase Transitions in Supersymmetric Quantum Electrodynamics With Resurgence Theory

2021 ◽  
Vol 1 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
Series Expansion ◽  
Quantum Electrodynamics ◽  
Quantum Field ◽  
Perturbative Series

Using resurgence theory to describe phase transitions in quantum field theory shows that information on non-perturbative effects like phase transitions can be obtained from a perturbative series expansion.

Quantum field theory (QFT) at finite temperature: Equilibrium properties

2021 ◽  
pp. 786-830
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
High Temperature ◽  
Dimensional Reduction ◽  
Finite Temperature ◽  
Finite Size ◽  
Quantum Field ◽  
Statistical Field ◽  
Statistical Field Theory

Some equilibrium properties in statistical quantum field theory (QFT), that is, relativistic QFT at finite temperature are reviewed. Study of QFT at finite temperature is motivated by cosmological problems, high energy heavy ion collisions, and speculations about possible phase transitions, also searched for in numerical simulations. In particular, the situation of finite temperature phase transitions, or the limit of high temperature (an ultra-relativistic limit where the temperature is much larger than the physical masses of particles) are discussed. The concept of dimensional reduction emerges, in many cases, statistical properties of finite-temperature QFT in (1, d − 1) dimensions can be described by an effective classical statistical field theory in (d − 1) dimensions. Dimensional reduction generalizes a property already observed in the non-relativistic example of the Bose gas, and indicates that quantum effects are less important at high temperature. The corresponding technical tools are a mode-expansion of fields in the Euclidean time variable, singling out the zero modes of boson fields, followed by a local expansion of the resulting (d − 1)-dimensional effective field theory (EFT). Additional physical intuition about QFT at finite temperature in (1, d−1) dimensions can be gained by considering it as a classical statistical field theory in d dimensions, with finite size in one dimension. This identification makes an analysis of finite temperature QFT in terms of the renormalization group (RG), and the theory of finite-size effects of the classical theory, possible. These ideas are illustrated with several simple examples, the φ4 field theory, the non-linear σ-model, the Gross–Neveu model and some gauge theories.

Quantum field theory of phase transitions in Fermi systems

1968 ◽  
Vol 17 (68) ◽  
pp. 509-562 ◽  
Author(s):  
R.D. Mattuck ◽  
Börje Johansson
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
Quantum Field ◽  
Fermi Systems

scholarly journals SURPRISES IN NONPERTURBATIVE DYNAMICS IN σ-MODEL AT FINITE DENSITY

2004 ◽  
Vol 19 (18) ◽  
pp. 1341-1356 ◽  
Author(s):  
V. P. GUSYNIN ◽  
V. A. MIRANSKY ◽  
I. A. SHOVKOVY
Keyword(s):  
Elementary Particle ◽  
Field Theory ◽  
Quantum Field Theory ◽  
Particle Physics ◽  
Chemical Potential ◽  
High Density ◽  
Quantum Field ◽  
Finite Density ◽  
Elementary Particle Physics ◽  
Kaon Condensate

The linear SU (2)L× SU (2)R σ-model occupies a unique place in elementary particle physics and quantum field theory. It has been recently realized that when a chemical potential for hypercharge is added, it becomes a toy model for the description of the dynamics of the kaon condensate in high density QCD. We review recent results in nonperturbative dynamics obtained in the ungauged and gauged versions of this model.

Compatibility between the Ginzburg–Landau model and finite-temperature quantum field theory

2016 ◽  
Vol 31 (40) ◽  
pp. 1650227 ◽  
Author(s):  
T. C. A. Calza ◽  
F. L. Cardoso ◽  
L. G. Cardoso ◽  
C. A. Linhares
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Scalar Fields ◽  
Quantum Field ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Large N ◽  
Range Of Values

The formalism of finite-temperature quantum field theory, as developed by Matsubara, is applied to a Hamiltonian of N scalar fields with a quartic self-interaction at large N. A renormalized expression in the lowest quantum approximation is obtained for the squared mass m2 of the field, as a function of the temperature T, from which we study the process of spontaneous symmetry breaking. We find that in a range of values around the critical temperature Tc, the squared mass can be approximated by a linear relation m2 [Formula: see text] (T − Tc). We thus demonstrate the compatibility of the finite-temperature formalism for scalar fields, in the vicinity of criticality, with respect to the Ginzburg–Landau model. We also discuss the effects caused by the presence of a chemical potential and of an external magnetic field applied to the finite-temperature system, which however do not affect the linearity of the relation between the squared mass and the temperature.

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