# Quantum Field Theory at Finite Temperature: An Introduction

@article{ZinnJustin2000QuantumFT, title={Quantum Field Theory at Finite Temperature: An Introduction}, author={Jean Zinn-Justin}, journal={arXiv: High Energy Physics - Phenomenology}, year={2000} }

In these notes we review some properties of Statistical Quantum Field Theory at equilibrium, i.e Quantum Field Theory at finite temperature. We explain the relation between finite temperature quantum field theory in (d,1) dimensions and statistical classical field theory in d+1 dimensions. This identification allows to analyze the finite temperature QFT in terms of the renormalization group and the theory of finite size effects of the classical theory. We discuss in particular the limit of high…

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## References

SHOWING 1-10 OF 61 REFERENCES

### Temperature Independent Renormalization of Finite Temperature Field Theory

- Physics
- 2000

Abstract. We analyze 4-dimensional massive
$ \varphi^4 $ theory at finite temperature T in the imaginary-time formalism. We present a rigorous proof that this quantum field theory is renormalizable,…

### Quantum Field Theory and Critical Phenomena

- Physics
- 2002

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…

### Large order behaviour of perturbation theory

- PhysicsQuantum Field Theory and Critical Phenomena
- 1990

### Vector models in the large $N$ limit: a few applications

- Physics
- 1998

In these lecture notes prepared for the 11th Taiwan Spring School, Taipei 1997}, and updated for the Saalburg summer school 1998, we review the solutions of O(N) or U(N) models in the large N limit…

### Phys. Rev

- Phys. Rev
- 1976

### Phys

- Rev. B14
- 1976

### Nucl

- Phys. B432 (1994) 127; P. Arnold and O. Espinosa, Phys. Rev. D47
- 1993

### Prog

- Phys. 42 (1979) 389; A. Hebecker, Z. Phys. C60 (1993) 271; J.O. Andersen, Phys. Rev. D59
- 1999

### Phys

- Rev. D9 (1974) 3312; S. Weinberg, Phys. Rev. D9
- 1974

### Phys

- Rev. D15 (1977) 2897; E. Brézin, J. Physique (Paris) 43 (1982) 15; H. Meyer-Ortmanns, H.J. Pirner and B.J. Schaefer, Phys. Lett. B311 (1993) 213; M. Reuter, N. Tetradis and C. Wetterich, Nucl. Phys. B401 (1993) 567, hepph/9301271; see also G. N. J. Aaos, A. P. C. Malbouisson, N. F. Svaiter, Nucl. Ph
- 1999