Path-integral quantization of Galilean Fermi fields

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.

LATEX file, 27 pages, 8 figures; typos in the journal version are removed, equation (1) in Introduction is corrected

References in corpus (5)

• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Exotic Galilean Conformal Symmetry and its Dynamical Realisations
• Nonrelativistic anyons in external electromagnetic field
• Enlarged Galilean symmetry of anyons and the Hall effect
• Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane

Cited by in corpus (6)

• Quantization of Interacting Galilean Field theories
• Galilean fermions: Classical and quantum aspects
• Weak-field approximation of effective gravitational theory with local Galilean invariance
• Teleparallel formalism of galilean gravity
• Non-relativistic Casimir effect at finite temperature
• Spin operator and spin states in Galilean covariant Fermi field theories