The Feynman chessboard model in 3 + 1 dimensions
The chessboard model was Feynman’s adaptation of his path integral method to a two-dimensional relativistic domain. It is shown that chessboard paths encode information about the contiguous pairs of paths in a spacetime plane, as required by discrete worldlines in Minkowski space. The application of...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2023-11-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2023.1286030/full |
| _version_ | 1797449153063682048 |
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| author | G. N. Ord |
| author_facet | G. N. Ord |
| author_sort | G. N. Ord |
| collection | DOAJ |
| description | The chessboard model was Feynman’s adaptation of his path integral method to a two-dimensional relativistic domain. It is shown that chessboard paths encode information about the contiguous pairs of paths in a spacetime plane, as required by discrete worldlines in Minkowski space. The application of coding by pairs in a four-dimensional spacetime is then restricted by the requirements of the Lorentz transformation, and the implementation of these restrictions provides an extension of the model to 4D, illuminating the relationship between relativity and quantum propagation. |
| first_indexed | 2024-03-09T14:21:36Z |
| format | Article |
| id | doaj.art-84312b4ff43d46a6b48eb054bfd713e0 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-03-09T14:21:36Z |
| publishDate | 2023-11-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-84312b4ff43d46a6b48eb054bfd713e02023-11-28T11:01:55ZengFrontiers Media S.A.Frontiers in Physics2296-424X2023-11-011110.3389/fphy.2023.12860301286030The Feynman chessboard model in 3 + 1 dimensionsG. N. OrdThe chessboard model was Feynman’s adaptation of his path integral method to a two-dimensional relativistic domain. It is shown that chessboard paths encode information about the contiguous pairs of paths in a spacetime plane, as required by discrete worldlines in Minkowski space. The application of coding by pairs in a four-dimensional spacetime is then restricted by the requirements of the Lorentz transformation, and the implementation of these restrictions provides an extension of the model to 4D, illuminating the relationship between relativity and quantum propagation.https://www.frontiersin.org/articles/10.3389/fphy.2023.1286030/fullquantum mechanicsspecial relativitystatistical mechanicspath integralsFeynman chessboard |
| spellingShingle | G. N. Ord The Feynman chessboard model in 3 + 1 dimensions Frontiers in Physics quantum mechanics special relativity statistical mechanics path integrals Feynman chessboard |
| title | The Feynman chessboard model in 3 + 1 dimensions |
| title_full | The Feynman chessboard model in 3 + 1 dimensions |
| title_fullStr | The Feynman chessboard model in 3 + 1 dimensions |
| title_full_unstemmed | The Feynman chessboard model in 3 + 1 dimensions |
| title_short | The Feynman chessboard model in 3 + 1 dimensions |
| title_sort | feynman chessboard model in 3 1 dimensions |
| topic | quantum mechanics special relativity statistical mechanics path integrals Feynman chessboard |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2023.1286030/full |
| work_keys_str_mv | AT gnord thefeynmanchessboardmodelin31dimensions AT gnord feynmanchessboardmodelin31dimensions |