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

M. Suleymanov; M. A. Zubkov

doi:https://doi.org/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

Ariel University

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

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

All Science Journal Classification (ASJC) codes

Nuclear and High Energy Physics

Access to Document

https://doi.org/10.1016/j.nuclphysb.2018.11.007

Cite this

@article{046d4cfdcec74189850cda063b887143,

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.",

author = "M. Suleymanov and Zubkov, {M. A.}",

note = "Publisher Copyright: {\textcopyright} 2018 The Author(s)",

year = "2019",

month = jan,

doi = "https://doi.org/10.1016/j.nuclphysb.2018.11.007",

language = "الإنجليزيّة",

volume = "938",

pages = "171--199",

journal = "Nuclear Physics B",

issn = "0550-3213",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field

AU - Suleymanov, M.

AU - Zubkov, M. A.

PY - 2019/1

Y1 - 2019/1

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.

UR - http://www.scopus.com/inward/record.url?scp=85056756256&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.nuclphysb.2018.11.007

DO - https://doi.org/10.1016/j.nuclphysb.2018.11.007

M3 - مقالة

SN - 0550-3213

VL - 938

SP - 171

EP - 199

JO - Nuclear Physics B

JF - Nuclear Physics B

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this