Path-integral quantization of Galilean Fermi fields

M. de Montigny; F. C. Khanna; F. M. Saradzhev

doi:10.1016/j.aop.2007.08.002

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arXiv · 0706.4106

Path-integral quantization of Galilean Fermi fields

M. de Montigny·F. C. Khanna·F. M. Saradzhev

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Abstract

The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. Firstly, we review the five-dimensional approach to the Galilean Dirac equation, which leads to the Levy-Leblond equations, and define the Galilean generating functional and Green's functions for positive- and negative-energy/mass solutions. Then, as an example of interactions, we consider the quartic self-interacting potential ${\lambda} (\bar{\Psi} {\Psi})^2$, and we derive expressions for the 2- and 4-point Green's functions. Our results are compatible with those found in the literature on non-relativistic many-body systems. The extended manifold allows for compact expressions of the contributions in $(3+1)$ space-time. This is particularly apparent when we represent the results with diagrams in the extended $(4+1)$ manifold, since they usually encompass more diagrams in Galilean $(3+1)$ space-time.

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M. de Montigny, F. C. Khanna, F. M. Saradzhev. 2007-06-27. Path-integral quantization of Galilean Fermi fields. https://doi.org/10.1016/j.aop.2007.08.002

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