Scattering in Algebraic Approach to Quantum Theory—Associative Algebras
The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula), and the inclusive scatte...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/12/660 |
| _version_ | 1797455021255688192 |
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| author | Albert Schwarz |
| author_facet | Albert Schwarz |
| author_sort | Albert Schwarz |
| collection | DOAJ |
| description | The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula), and the inclusive scattering matrix is expressed in terms of generalized Green functions on shell. The expression for inclusive scattering matrix can be used also for quasi-particles (for elementary excitations of any translation-invariant stationary state, for example, for elementary excitations of equilibrium state). An interesting novelty is the consideration of associative algebras over real numbers. |
| first_indexed | 2024-03-09T15:46:31Z |
| format | Article |
| id | doaj.art-3459476ff3cd4db0bfb70fc74236bb67 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T15:46:31Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-3459476ff3cd4db0bfb70fc74236bb672023-11-24T18:29:43ZengMDPI AGUniverse2218-19972022-12-0181266010.3390/universe8120660Scattering in Algebraic Approach to Quantum Theory—Associative AlgebrasAlbert Schwarz0Department of Mathematics, University of California, Davis, CA 95616, USAThe definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula), and the inclusive scattering matrix is expressed in terms of generalized Green functions on shell. The expression for inclusive scattering matrix can be used also for quasi-particles (for elementary excitations of any translation-invariant stationary state, for example, for elementary excitations of equilibrium state). An interesting novelty is the consideration of associative algebras over real numbers.https://www.mdpi.com/2218-1997/8/12/660inclusive scattering matrixgeneralized Green functionsassociative algebras |
| spellingShingle | Albert Schwarz Scattering in Algebraic Approach to Quantum Theory—Associative Algebras Universe inclusive scattering matrix generalized Green functions associative algebras |
| title | Scattering in Algebraic Approach to Quantum Theory—Associative Algebras |
| title_full | Scattering in Algebraic Approach to Quantum Theory—Associative Algebras |
| title_fullStr | Scattering in Algebraic Approach to Quantum Theory—Associative Algebras |
| title_full_unstemmed | Scattering in Algebraic Approach to Quantum Theory—Associative Algebras |
| title_short | Scattering in Algebraic Approach to Quantum Theory—Associative Algebras |
| title_sort | scattering in algebraic approach to quantum theory associative algebras |
| topic | inclusive scattering matrix generalized Green functions associative algebras |
| url | https://www.mdpi.com/2218-1997/8/12/660 |
| work_keys_str_mv | AT albertschwarz scatteringinalgebraicapproachtoquantumtheoryassociativealgebras |