Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path-integral quantization of Galilean Fermi fields   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.

4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat