TY - JOUR

T1 - Feynman rules in terms of the Wigner transformed Green functions

AU - Zhang, C. X.

AU - Zubkov, M. A.

N1 - Publisher Copyright:
© 2020 The Author(s)

PY - 2020/3/10

Y1 - 2020/3/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85077653070&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2020.135197

DO - 10.1016/j.physletb.2020.135197

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85077653070

SN - 0370-2693

VL - 802

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

M1 - 135197

ER -