Real time statistical field theory

Abstract

We have written a {\it Mathematica} program that calculates the integrand corresponding to any amplitude in the closed-time-path formulation of real time statistical field theory. The program is designed so that it can be used by someone with no previous experience with {\it Mathematica}. It performs the contractions over the tensor indices that appear in real time statistical field theory and gives the result in the 1-2, Keldysh or RA basis. We have used the program to calculate the ward identity for the QED 3-point function, the QED 4-point function for two photons and two fermions, and the QED 5-point function for three photons and two fermions. In real time statistical field theory, there are seven 3-point functions, 15 4-point functions and 31 5-point functions. We produce a table that gives the results for all of these functions. In addition, we give a simple general expression for the KMS conditions between $n$-point green functions and vertex functions, in both the Keldysh and RA bases

25 pages, 12 figures

References in corpus (9)

• Advances in perturbative thermal field theory
• A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions
• Cutting rules in the real time formalisms at finite temperature
• Scattering amplitudes at finite temperature
• Four-Point Spectral Functions and Ward Identities in Hot QED
• Ward Identities in Non-equilibrium QED
• KMS conditions for 4-point Green functions at finite temperature
• Evaluating Real Time Finite Temperature Feynman Amplitudes
• A New Formulation of a 1+1 Dimensional Field Theory Constrained to a Box

Cited by in corpus (16)

• Thermal out-of-time-order correlators, KMS relations, and spectral functions
• Holographic Brownian Motion and Time Scales in Strongly Coupled Plasmas
• Kubo formulae for the shear and bulk viscosity relaxation times and the scalar field theory shear ${\tau }_{\pi }$ calculation
• Leading Order QCD Shear Viscosity from the 3PI Effective Action
• QED Electrical Conductivity using the 2PI Effective Action
• The fermion mass at next-to-leading order in the HTL effective theory
• Spectral Representation of Thermal OTO Correlators
• Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma
• The HTL Lagrangian at NLO: the photon case
• Energetic di-leptons from the Quark Gluon Plasma
• Collective modes in anisotropic plasmas
• Thermal field theory at next-to-leading order in the hard thermal loop expansion
• Keldysh functional renormalization group for electronic properties of graphene
• NLO quark self-energy and dispersion relation using the hard thermal loop resummation
• Effective Coupling Constant of Plasmons
• NLO Dispersion Laws for Slow-Moving Quarks in HTL QCD