Wigner-Weyl formalism for the lattice models

Michael Suleymanov, Mikhail Zubkov

Research output: Contribution to journalArticlepeer-review


We discuss application of Wigner-Weyl formalism to the lattice models of condensed matter physics and relativistic quantum field theory. For the noninteracting models our technique relates Wigner transformation of the fermionic Green's function with the Weyl symbol QW of lattice Dirac operator. We take as an example of the model defined on rectangular lattice the model of Wilson fermions. It represents the regularization of relativistic quantum field theory and, in addition, describes qualitatively certain topological materials in condensed matter physics. In this model we derive expression for QW in the presence of the most general case of external U(1) gauge field. Next, we solve the Groenewold equation to all orders in powers of the derivatives of QW.

Original languageEnglish
Article number2044033
JournalInternational Journal of Modern Physics A
Issue number25
StatePublished - 10 Sep 2021
Externally publishedYes

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  • Wigner-Weyl calculus
  • Wilson fermions
  • lattice models


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