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.

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.

scholarly journals Galilean covariance, Casimir effect and Stefan–Boltzmann law at finite temperature

2017 ◽  
Vol 32 (16) ◽  
pp. 1750094 ◽  
Author(s):  
S. C. Ulhoa ◽  
A. F. Santos ◽  
Faqir C. Khanna
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Temperature ◽  
Temperature Effects ◽  
Casimir Effect ◽  
Quantum Field ◽  
Covariant Quantum ◽  
Thermo Field Dynamics ◽  
Boltzmann Law ◽  
Galilean Covariance

The Galilean covariance, formulated in 5-dimensions space, describes the nonrelativistic physics in a way similar to a Lorentz covariant quantum field theory being considered for relativistic physics. Using a nonrelativistic approach the Stefan–Boltzmann law and the Casimir effect at finite temperature for a particle with spin zero and 1/2 are calculated. The thermo field dynamics is used to include the finite temperature effects.

REGULARIZATION OF GENERAL MULTIDIMENSIONAL EPSTEIN ZETA-FUNCTIONS

1989 ◽  
Vol 01 (01) ◽  
pp. 113-128 ◽  
Author(s):  
E. ELIZALDE ◽  
A. ROMEO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Partition Function ◽  
Zeta Function ◽  
Finite Temperature ◽  
Casimir Effect ◽  
Zeta Functions ◽  
Quantum Field ◽  
Type Formula

We study expressions for the regularization of general multidimensional Epstein zeta-functions of the type [Formula: see text] After reviewing some classical results in the light of the extended proof of zeta-function regularization recently obtained by the authors, approximate but very quickly convergent expressions for these functions are derived. This type of analysis has many interesting applications, e.g. in any quantum field theory defined in a partially compactified Euclidean spacetime or at finite temperature. As an example, we obtain the partition function for the Casimir effect at finite temperature.

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