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Index summation in real time statistical field theory.

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Title: Index summation in real time statistical field theory.
Authors: Carrington, M.E.1,2 carrington@brandonu.ca, Fugleberg, T.1,2 fuglebergt@brandonu.ca, Irvine, D.S.3 sammy@hotmail.com, Pickering, D.3 pickering@brandonu.ca
Source: European Physical Journal C -- Particles & Fields. Apr2007, Vol. 50 Issue 3, p711-727. 17p. 14 Diagrams.
Subjects: Wolfram language (Computer program language), Field theory (Physics), Physics, Particles (Nuclear physics), Physical sciences
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. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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