Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field

M. Suleymanov; M. A. Zubkov

doi:10.1016/j.nuclphysb.2018.11.007

Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field

M. Suleymanov, M. A. Zubkov

Department of Physics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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 Q_W of Wilson Dirac operator. We derive the simple expression for Q_W 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 Q_W. 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.

Original language	English
Pages (from-to)	171-199
Number of pages	29
Journal	Nuclear Physics B
Volume	938
DOIs	https://doi.org/10.1016/j.nuclphysb.2018.11.007
State	Published - Jan 2019

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10.1016/j.nuclphysb.2018.11.007

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title = "Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field",

abstract = "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.",

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N2 - 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.

AB - 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.

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Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field

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