Feynman checkers: lattice quantum field theory with real time
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866908329825009664 |
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| author | Skopenkov, Mikhail Ustinov, Alexey |
| author_facet | Skopenkov, Mikhail Ustinov, Alexey |
| contents | We present a new completely elementary model that describes the creation, annihilation, and motion of non-interacting electrons and positrons along a line. It is a modification of the model known under the names Feynman checkers or one-dimensional quantum walk. It can be viewed as a six-vertex model with certain complex weights of the vertices. The discrete model is consistent with the continuum quantum field theory, namely, reproduces the known expected charge density as the lattice step tends to zero. It is exactly solvable in terms of hypergeometric functions. We introduce interaction resembling Fermi's theory and establish perturbation expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14247 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Feynman checkers: lattice quantum field theory with real time Skopenkov, Mikhail Ustinov, Alexey Mathematical Physics Classical Analysis and ODEs Combinatorics 81T25, 81T27, 81T40, 82B20, 82B23, 33C45 We present a new completely elementary model that describes the creation, annihilation, and motion of non-interacting electrons and positrons along a line. It is a modification of the model known under the names Feynman checkers or one-dimensional quantum walk. It can be viewed as a six-vertex model with certain complex weights of the vertices. The discrete model is consistent with the continuum quantum field theory, namely, reproduces the known expected charge density as the lattice step tends to zero. It is exactly solvable in terms of hypergeometric functions. We introduce interaction resembling Fermi's theory and establish perturbation expansion. |
| title | Feynman checkers: lattice quantum field theory with real time |
| topic | Mathematical Physics Classical Analysis and ODEs Combinatorics 81T25, 81T27, 81T40, 82B20, 82B23, 33C45 |
| url | https://arxiv.org/abs/2208.14247 |