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arXiv · hep-ph/0608298

Real time statistical field theory

M. E. Carrington·T. Fugleberg·D. S. Irvine·D. Pickering
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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

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M. E. Carrington, T. Fugleberg, D. S. Irvine, D. Pickering. 2006-08-28. Real time statistical field theory. https://doi.org/10.1140/epjc%2Fs10052-007-0276-9

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