Gauge invariance and reciprocity in quantum mechanics

Journal Article · Mon Mar 15 04:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.032107· OSTI ID:21408366

Leung, P T ^[1]; Young, K ^[2]

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1. Institute of Optoelectronic Sciences, National Taiwan Ocean University, Keelung, Taiwan (China)
2. Department of Physics, Chinese University of Hong Kong (Hong Kong)

Reciprocity in wave propagation usually refers to the symmetry of the Green's function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. Several possible alternative criteria are given and analyzed with reference to different examples with nonzero magnetic fields and/or vector potentials, including the case of a multiply connected spatial domain. It is shown that the appropriate reciprocity criterion allows for specific phase factors separable into functions of the source and observer coordinates and that this condition is robust with respect to the addition of any scalar potential. In the Aharonov-Bohm effect, reciprocity beyond monoenergetic experiments holds only because of subsidiary conditions satisfied in actual experiments: the test charge is in units of e and the flux is produced by a condensate of particles with charge 2e.

• OSTI ID: 21408366
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
AHARONOV-BOHM EFFECT
COORDINATES
DIMENSIONLESS NUMBERS
FUNCTIONS
GAUGE INVARIANCE
GREEN FUNCTION
INVARIANCE PRINCIPLES
MAGNETIC FIELDS
MECHANICS
POTENTIALS
POWER FACTOR
QUANTUM MECHANICS
SCALARS
SYMMETRY
WAVE PROPAGATION