## Finite Temperature Field TheoryThis book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. Applications of the formalisms are worked out in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The question of gauge dependence of the effective potential and the Nielsen identities are explained. The nonrestoration of some symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are also described thoroughly. Other topics include (1+1)- and (2+1)-dimensional field theories at finite temperature and phase transitions, derivative expansion, linear response theory and the question of infrared divergences at finite temperature. In addition, examples of nonequilibrium phenomena are discussed with the disoriented chiral condensates as an illustration.This book is a very useful tool for graduate students, teachers and researchers in theoretical physics. |

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### Contents

Chapter 2 Real Time Formalism | 39 |

Chapter 3 Thermofield Dynamics | 69 |

Chapter 4 Gauge Theories | 105 |

Chapter 5 Cutting Rules at T 0
| 149 |

Chapter 6 Symmetry Breaking | 191 |

Chapter 7 Nielsen Identities | 233 |

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### Common terms and phrases

amplitude analytic anti-commutation auxiliary field Bogoliubov transformation bosons and fermions boundary conditions BRST calculation chapter chiral symmetry circled closed time path con coordinate define density in eq derivative expansion diagrams discussion effective potential energy equation evaluated fact fermion condensate fermion fields Feynman field variables finite temperature follows Furthermore gauge dependent gauge fields gauge fixing gauge theory ghost fields global symmetry Goldstino Greens functions Hamiltonian Hilbert space imaginary time formalism interactions Lagrangian density let us note loop mass massless matrix momentum space nonanalytic nontrivial note from eq obtain parameter particles partition function path integral Phys point function propagator QBRST quantum field theory real time formalism represents satisfy scalar field self-energy spontaneously broken supersymmetric theory supersymmetry symmetry breaking takes the form tem temperature dependent thermal indices thermal vacuum thermofield dynamics tilde transformation tree level uncircled vertices vacuum expectation value vanish vertex Ward identities write zero temperature