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

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.

Phase transitions in quantum field theory. I. Phases of the Thirring model

1979 ◽  
Vol 123 (1) ◽  
pp. 24-35 ◽  
Author(s):  
H.S Sharatchandra ◽  
P Mitra
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
Thirring Model ◽  
Quantum Field

Finite temperature phase transitions in quantum field theory

1993 ◽  
Vol 10 (S) ◽  
pp. S243-S244 ◽  
Author(s):  
D O'Connor ◽  
C R Stephens ◽  
F Freire
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
Finite Temperature ◽  
Temperature Phase ◽  
Quantum Field

Quantum Field Theory and Critical Phenomena

2021 ◽  
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
Critical Phenomena ◽  
Particle Physics ◽  
High Energy ◽  
Fine Tuning ◽  
High Energy Particle ◽  
Condensation Temperature ◽  
Quantum Field

Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamic (QED) has been the first example of a quantum field theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. In fact, as hopefully this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, although excellent textbooks about QFT had already been published, I thought, many years ago, that it might not be completely worthless to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group (RG) properties are systematically discussed. The notion of effective field theory (EFT) and the emergence of renormalizable theories are described. The consequences for fine-tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised.

Sign in / Sign up

Export Citation Format

Share Document