Corrigendum to “Wigner–Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field” [Nucl. Phys. B 938 (2019) 171–199]

2020

Nuclear Physics B

Self Cite

“…The proof is given in [38]. We repeat it here briefly This results in the factor 2 D in the third line.…”

Section: B-symbol Of Unity and The Other Examplesmentioning

confidence: 82%

“…Following [35,38,78,79] we start with the lattice tight-binding fermionic model with the partition function of the following form…”

Section: A Lattice Model In Momentum Spacementioning

confidence: 99%

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Precise Wigner-Weyl calculus for lattice models

Fialkovsky

2020

Nuclear Physics B

Self Cite

“…It satisfies the Groenewold equation Q W (R, p) ⋆ G W (R, p) = 1 [13,38], where Q W is the Weyl symbol of operatorQ,…”

Section: Wigner Transform and The Model Under Considerationmentioning

confidence: 99%

“…φ is the inverse bare propagator, and the Wigner -transformed Green function D W satisfies U W (R, p) ⋆ D W (R, p) = 1. An important result of Wigner -Weyl calculus is [38][39][40] C(x 1 ,…”

Section: Wigner Transform and The Model Under Considerationmentioning

confidence: 99%

Feynman rules in terms of the Wigner transformed Green functions

Zhang

2020

Physics Letters B

Self Cite

In the models defined on the inhomogeneous background the propagators depend on the two space -time momenta rather than on one momentum as in the homogeneous systems. Therefore, the conventional Feynman diagrams contain extra integrations over momenta, which complicate calculations. We propose to express all amplitudes through the Wigner transformed propagators. This approach allows us to reduce the number of integrations. As a price for this the ordinary products of functions are replaced by the Moyal products. The corresponding rules of the diagram technique are formulated using an example of the model with the fermions interacting via an exchange by scalar bosons. The extension of these rules to the other models is straightforward. This approach may simplify calculations in certain particular cases. The most evident one is the calculation of various non -dissipative currents.

The type II Weyl semimetals at low temperatures: Chiral anomaly, elastic deformations, zero sound

Lewkowicz

2018

Annals of Physics

We consider the properties of the type II Weyl semimetals at low temperatures basing on the particular tight -binding model. In the presence of electric field directed along the line connecting the Weyl points of opposite chirality the occupied states flow along this axis giving rise to the creation of electron -hole pairs. The electrons belong to a vicinity of one of the two type II Weyl points while the holes belong to the vicinity of the other. This process may be considered as the manifestation of the chiral anomaly that exists without any external magnetic field. It may be observed experimentally through the measurement of conductivity. Next, we consider the modification of the theory in the presence of elastic deformations. In the domain of the considered model, where it describes the type I Weyl semimetals the elastic deformations lead to the appearance of emergent gravity. In the domain of the type II Weyl semimetals the form of the Fermi surface is changed due to the elastic deformations, and its fluctuations represent the special modes of the zero sound. We find that there is one -to one correspondence between them and the sound waves of the elasticity theory. Next, we discuss the influence of the elastic deformations on the conductivity. The particularly interesting case is when our model describes the intermediate state between the type I and the type II Weyl semimetal. Then without the elastic deformations there are the Fermi lines instead of the Fermi points/Fermi surface, while the DC conductivity vanishes. However, even small elastic deformations may lead to the appearance of large conductivity.