Canonical quantization of Galilean covariant field theories
Abstract
The Galileaninvariant field theories are quantized by using the canonical method and the fivedimensional Lorentzlike covariant expressions of nonrelativistic field equations. This method is motivated by the fact that the extended Galilei group in 3 + 1 dimensions is a subgroup of the inhomogeneous Lorentz group in 4 + 1 dimensions. First, we consider complex scalar fields, where the Schroedinger field follows from a reduction of the KleinGordon equation in the extended space. The underlying discrete symmetries are discussed, and we calculate the scattering crosssections for the Coulomb interaction and for the selfinteracting term {lambda}{phi} {sup 4}. Then, we turn to the Dirac equation, which, upon dimensional reduction, leads to the LevyLeblond equations. Like its relativistic analogue, the model allows for the existence of antiparticles. Scattering amplitudes and crosssections are calculated for the Coulomb interaction, the electronelectron and the electronpositron scattering. These examples show that the socalled 'nonrelativistic' approximations, obtained in lowvelocity limits, must be treated with great care to be Galileiinvariant. The nonrelativistic Proca field is discussed briefly.
 Authors:

 Theoretical Physics Institute, University of Alberta, Edmonton, Alta., T6G 2J1 (Canada)
 Theoretical Physics Institute, University of Alberta, Edmonton, Alta., T6G 2J1 (Canada) and Faculte SaintJean, University of Alberta, Edmonton, Alta., T6C 4G9 (Canada)
 Theoretical Physics Institute, University of Alberta, Edmonton, Alta., T6G 2J1 (Canada) and TRIUMF, 4004, Wesbrook Mall, Vancouver, BC, V6T 2A3 (Canada)
 Publication Date:
 OSTI Identifier:
 20690201
 Resource Type:
 Journal Article
 Journal Name:
 Annals of Physics (New York)
 Additional Journal Information:
 Journal Volume: 320; Journal Issue: 1; Other Information: DOI: 10.1016/j.aop.2005.04.013; PII: S00034916(05)000680; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 00034916
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANTIPARTICLES; CROSS SECTIONS; DIRAC EQUATION; ELECTRONPOSITRON COLLISIONS; ELECTRONPOSITRON INTERACTIONS; ELECTRONS; FIELD THEORIES; KLEINGORDON EQUATION; LORENTZ GROUPS; MATHEMATICAL SPACE; QUANTIZATION; RELATIVISTIC RANGE; SCALAR FIELDS; SCATTERING; SCATTERING AMPLITUDES; SYMMETRY
Citation Formats
Santos, E S, Montigny, M de, and Khanna, F C. Canonical quantization of Galilean covariant field theories. United States: N. p., 2005.
Web. doi:10.1016/j.aop.2005.04.013.
Santos, E S, Montigny, M de, & Khanna, F C. Canonical quantization of Galilean covariant field theories. United States. https://doi.org/10.1016/j.aop.2005.04.013
Santos, E S, Montigny, M de, and Khanna, F C. Tue .
"Canonical quantization of Galilean covariant field theories". United States. https://doi.org/10.1016/j.aop.2005.04.013.
@article{osti_20690201,
title = {Canonical quantization of Galilean covariant field theories},
author = {Santos, E S and Montigny, M de and Khanna, F C},
abstractNote = {The Galileaninvariant field theories are quantized by using the canonical method and the fivedimensional Lorentzlike covariant expressions of nonrelativistic field equations. This method is motivated by the fact that the extended Galilei group in 3 + 1 dimensions is a subgroup of the inhomogeneous Lorentz group in 4 + 1 dimensions. First, we consider complex scalar fields, where the Schroedinger field follows from a reduction of the KleinGordon equation in the extended space. The underlying discrete symmetries are discussed, and we calculate the scattering crosssections for the Coulomb interaction and for the selfinteracting term {lambda}{phi} {sup 4}. Then, we turn to the Dirac equation, which, upon dimensional reduction, leads to the LevyLeblond equations. Like its relativistic analogue, the model allows for the existence of antiparticles. Scattering amplitudes and crosssections are calculated for the Coulomb interaction, the electronelectron and the electronpositron scattering. These examples show that the socalled 'nonrelativistic' approximations, obtained in lowvelocity limits, must be treated with great care to be Galileiinvariant. The nonrelativistic Proca field is discussed briefly.},
doi = {10.1016/j.aop.2005.04.013},
url = {https://www.osti.gov/biblio/20690201},
journal = {Annals of Physics (New York)},
issn = {00034916},
number = 1,
volume = 320,
place = {United States},
year = {2005},
month = {11}
}