The European Physical Journal C

, Volume 50, Issue 3, pp 711–727 | Cite as

Index summation in real time statistical field theory

  • M.E. CarringtonEmail author
  • T. Fugleberg
  • D.S. Irvine
  • D. Pickering
Special Article - Tools for Experiment and Theory


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.


Ward Identity Vertex Function Araa Index Summation External Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • M.E. Carrington
    • 1
    • 2
    Email author
  • T. Fugleberg
    • 1
    • 2
  • D.S. Irvine
    • 3
  • D. Pickering
    • 3
  1. 1.Department of PhysicsBrandon UniversityBrandonCanada
  2. 2.Winnipeg Institute for Theoretical PhysicsWinnipegCanada
  3. 3.Department of MathematicsBrandon UniversityBrandonCanada

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