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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211624 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862618700579864576 |
|---|---|
| author | Gough, John E. |
| author_facet | Gough, John E. |
| citation_txt | Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams. John E. Gough. SIGMA 18 (2022), 044, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2026-03-14T10:56:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211624 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T10:56:31Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gough, John E. 2026-01-07T13:40:14Z 2022 Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams. John E. Gough. SIGMA 18 (2022), 044, 15 pages 1815-0659 2020 Mathematics Subject Classification: 81T18; 05C75; 81S25 arXiv:2203.09296 https://nasplib.isofts.kiev.ua/handle/123456789/211624 https://doi.org/10.3842/SIGMA.2022.044 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. I would like to thank the anonymous referee who pointed out an issue with the original text presented here as Remark 1.5. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams Article published earlier |
| spellingShingle | Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams Gough, John E. |
| title | Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams |
| title_full | Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams |
| title_fullStr | Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams |
| title_full_unstemmed | Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams |
| title_short | Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams |
| title_sort | field calculus: quantum and statistical field theory without the feynman diagrams |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211624 |
| work_keys_str_mv | AT goughjohne fieldcalculusquantumandstatisticalfieldtheorywithoutthefeynmandiagrams |