Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annals of Physics

Galilei-covariant path-integral quantization of non-relativistic complex scalar fields

Luciano M. Abreu, M. de Montigny, F. C. Khanna, Ademir Eugenio de Santana

Published Jul 22, 2003• 14 citations
Publisher
DOI
10.1016/s0003-4916(03)00140-4

Related papers

Path-integral quantization of Galilean Fermi fields 1

M. de Montigny, F. C. Khanna, Fuad M. Saradzhev

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 Lévy-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 λ(ΨΨ) 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. 1

•Dec 4, 2012•5 citations

Path-integral quantization of Galilean Fermi fields

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

arXiv:0706.4106•Annals of Physics•Aug 15, 2007•9 citations

THE USE OF NON-RELATIVISTIC PATH INTEGRALS IN FIELD THEORIES

I. H. Duru

WORLD SCIENTIFIC eBooks•Jun 1, 2001•0 citations

Galilei covariance and quasi-free representations of Fermi fields

K. Kraus, H -G Stark

Some quasi-free irreducible representations of the CAR algebra of a non-relativistic free Fermi field are constructed, which are covariant under certain subgroups of the extended Galilei group. The construction of fully covariant (but reducible) representations as direct integrals of partially covariant ones is described. This method is also applicable to arbitrary C*-algebras and other covariance groups.

Journal of Physics A Mathematical and General•Jul 1, 1982•2 citations

Path integrals and boundary conditions

M. Asorey, Alberto Ibort, Giuseppe Marmo

The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange formalism preserves relativistic covariance which makes the Feynman method very convenient to achieve the renormalization of field theories both in perturbative and non-perturbative approaches. However, when the systems are confined in bounded domains we shall show that the path integral approach does not describe the most general type of boundary conditions. Highly non-local boundary conditions cannot be described by Feynman's approach. We analyse in this note the origin of this problem in quantum mechanics and its implications for field theory.

arXiv:quant-ph/0609023•Sep 4, 2006•4 citations

Path Integrals in Relativistic Quantum Mechanics

Gian Fabrizio De Angelis, Maurizio Serva

QP-PQ, quantum probability and white noise analysis•Jul 4, 1994•0 citations
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 Lévy-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 λ(ΨΨ) 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. 1
The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange formalism preserves relativistic covariance which makes the Feynman method very convenient to achieve the renormalization of field theories both in perturbative and non-perturbative approaches. However, when the systems are confined in bounded domains we shall show that the path integral approach does not describe the most general type of boundary conditions. Highly non-local boundary conditions cannot be described by Feynman's approach. We analyse in this note the origin of this problem in quantum mechanics and its implications for field theory.