Index summation in real time statistical field theory |
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Authors: | ME Carrington T Fugleberg DS Irvine D Pickering |
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Institution: | (1) Department of Physics, Brandon University, Brandon, Manitoba, R7A 6A9, Canada;(2) Winnipeg Institute for Theoretical Physics, Winnipeg, Manitoba, Canada;(3) Department of Mathematics, Brandon University, Brandon, Manitoba, R7A 6A9, Canada |
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Abstract: | We have written a 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 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. The program treats all fields as scalars, but the result can be applied to theories with
dirac and lorentz structure by making simple adjustments. As an example, 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.
PACS 11.10.Wx; 11.15.-q |
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Keywords: | |
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