Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams

For a given base space (spacetime), we consider the Guichardet space over the Guichardet space over . Here we develop a ''field calculus'' based on the Guichardet integral. This is the natural setting in which to describe Green function relations for Boson systems. Here we can f...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2022
Main Author: Gough, John E.
Format: Article
Language:English
Published: Інститут математики НАН України 2022
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211624
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams. John E. Gough. SIGMA 18 (2022), 044, 15 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:For a given base space (spacetime), we consider the Guichardet space over the Guichardet space over . Here we develop a ''field calculus'' based on the Guichardet integral. This is the natural setting in which to describe Green function relations for Boson systems. Here we can follow the suggestion of Schwinger and develop a differential (local field) approach rather than the integral one pioneered by Feynman. This is helped by a DEFG (Dyson-Einstein-Feynman-Guichardet) shorthand, which greatly simplifies expressions. This gives a convenient framework for the formal approach of Schwinger and Tomonaga as opposed to Feynman diagrams. The Dyson-Schwinger is recast in this language with the help of bosonic creation/annihilation operators. We also give the combinatorial approach to tree-expansions.
ISSN:1815-0659