On Galilei Invariance in Quantum Mechanics and the Bargmann Superselection Rule

✍ Scribed by Domenico Giulini

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 578 KB
• Volume: 249
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1996.0069

✦ Synopsis

We reinvestigate Bargmann's superselection rule for the overall mass of n particles in ordinary quantum mechanics with Galilei invariant interaction potential. We point out that in order for mass to define a superselection rule it should be considered as a dynamical variable. We present a minimal extension of the original dynamics in which mass it treated as dynamical variable. Here the classical symmetry group turns out to be given by an R-extension of the Galilei group. Unlike before, there is now no obstruction to implement an action of the classical symmetry group on Hilbert space. We include some comments of a general nature on formal derivations of superselection rules without dynamical context. 1996 Academic Press, Inc.

M and M$ . But precisely what is that system? In ordinary quantum mechanics, the masses are fixed parameters which do not label different states but rather belong to the specification of the system. In other words, two n-particle systems with different overall mass are really considered to be different systems. In order to article no.