scholarly journals Methods of Quantum Field Theory in Condensed Matter Physics

1984 ◽  
Vol 80 ◽  
pp. 26-39 ◽  
Author(s):  
Hiroomi Umezawa
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Condensed Matter ◽  
Condensed Matter Physics ◽  
Quantum Field

Quantum Field Theory in Condensed Matter Physics

Physics Today ◽  
1997 ◽  
Vol 50 (2) ◽  
pp. 66-66 ◽  
Author(s):  
Alexi M. Tsvelik ◽  
Allan Macdonald
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Condensed Matter ◽  
Condensed Matter Physics ◽  
Quantum Field

Wigner–Weyl formalism for the lattice models

2021 ◽  
pp. 2044033
Author(s):  
Michael Suleymanov ◽  
Mikhail Zubkov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Condensed Matter ◽  
Relativistic Quantum ◽  
Lattice Models ◽  
Rectangular Lattice ◽  
Condensed Matter Physics ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Weyl Symbol

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 [Formula: see text] 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 [Formula: see text] in the presence of the most general case of external [Formula: see text] gauge field. Next, we solve the Groenewold equation to all orders in powers of the derivatives of [Formula: see text].

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