Galilean and U(1)-gauge symmetry of the Schroedinger field

Journal Article · Mon Dec 15 00:00:00 EST 2008 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2008.05.001· OSTI ID:21167685

Wickramasekara, S ^[1]

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1. Department of Physics, Grinnell College, Grinnell, IA 50112 (United States)

This paper undertakes a study of the nature of the force associated with the local U(1)-gauge symmetry of a non-relativistic quantum particle. To ensure invariance under local U(1) symmetry, a matter field must couple to a gauge field. We show that such a gauge field satisfies Maxwell's equations, whether the matter field coupled to it is relativistic or non-relativistic. This result suggests that the structure of Maxwell's equations is determined by gauge symmetry rather than the symmetry transformation properties of space-time. In order to assess the validity of this notion, we examine the transformation properties of the coupled matter and gauge fields under Galilean transformations. Our main technical result is the Galilean invariance of the full equations of motion of the U(1) gauge field.

• OSTI ID: 21167685
• Journal Information: Annals of Physics (New York), Vol. 323, Issue 12; Other Information: DOI: 10.1016/j.aop.2008.05.001; PII: S0003-4916(08)00073-0; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS OF MOTION
GALILEI TRANSFORMATIONS
GAUGE INVARIANCE
MAXWELL EQUATIONS
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
SCHROEDINGER PICTURE
SPACE-TIME
U-1 GROUPS