Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field
We develop Wigner–Weyl formalism for the lattice models. For the definiteness we consider Wilson fermions in the presence of U(1) gauge field. The given technique reduces calculation of the two point fermionic Green function to solution of the Groenewold equation. It relates Wigner transformation of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2019-01-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321318303171 |
| _version_ | 1819224883424395264 |
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| author | M. Suleymanov M.A. Zubkov |
| author_facet | M. Suleymanov M.A. Zubkov |
| author_sort | M. Suleymanov |
| collection | DOAJ |
| description | We develop Wigner–Weyl formalism for the lattice models. For the definiteness we consider Wilson fermions in the presence of U(1) gauge field. The given technique reduces calculation of the two point fermionic Green function to solution of the Groenewold equation. It relates Wigner transformation of the Green function with the Weyl symbol QW of Wilson Dirac operator. We derive the simple expression for QW in the presence of varying external U(1) gauge field. Next, we solve the Groenewold equation to all orders in powers of the derivatives of QW. Thus the given technique allows to calculate the fermion propagator in the lattice model with Wilson fermions in the presence of arbitrary background electromagnetic field. The generalization of this method to the other lattice models is straightforward. |
| first_indexed | 2024-12-23T10:00:47Z |
| format | Article |
| id | doaj.art-bd7959fad057407faef4d976aed3b659 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-23T10:00:47Z |
| publishDate | 2019-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-bd7959fad057407faef4d976aed3b6592022-12-21T17:51:15ZengElsevierNuclear Physics B0550-32132019-01-01938171199Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic fieldM. Suleymanov0M.A. Zubkov1Physics Department, Ariel University, Ariel 40700, IsraelCorresponding author.; Physics Department, Ariel University, Ariel 40700, IsraelWe develop Wigner–Weyl formalism for the lattice models. For the definiteness we consider Wilson fermions in the presence of U(1) gauge field. The given technique reduces calculation of the two point fermionic Green function to solution of the Groenewold equation. It relates Wigner transformation of the Green function with the Weyl symbol QW of Wilson Dirac operator. We derive the simple expression for QW in the presence of varying external U(1) gauge field. Next, we solve the Groenewold equation to all orders in powers of the derivatives of QW. Thus the given technique allows to calculate the fermion propagator in the lattice model with Wilson fermions in the presence of arbitrary background electromagnetic field. The generalization of this method to the other lattice models is straightforward.http://www.sciencedirect.com/science/article/pii/S0550321318303171 |
| spellingShingle | M. Suleymanov M.A. Zubkov Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field Nuclear Physics B |
| title | Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field |
| title_full | Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field |
| title_fullStr | Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field |
| title_full_unstemmed | Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field |
| title_short | Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field |
| title_sort | wigner weyl formalism and the propagator of wilson fermions in the presence of varying external electromagnetic field |
| url | http://www.sciencedirect.com/science/article/pii/S0550321318303171 |
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