Representations of the Galilei group View Full Text


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Article Info

DATE

1952-08

AUTHORS

E. Inönü, E. P. Wigner

ABSTRACT

While the transition to a moving coordinate system (x→x+vt, t→t) commutes in classical mechanics with displacements (x→x+a, t→t), the corresponding operations in Schrödinger's nonrelativistic wave mechanics do not commute. In fact, the two operations, taken in different orders, differ by a factor exp [imv÷a/h]. The present article considers the possibility of a nonrelativistic wave mechanics in which the transformations of the wave functions obey the same commutation relations as the transformations themselves. It shows that in such a mechanics position and momentum operators can exist only if it is reducible, i.e. only if the set of all states can be decomposed into subsets which are themselves invariant with respect to all permissible transformations of classical mechanics (rotations, displacements, proper Galilei transformations). More... »

PAGES

705-718

Journal

TITLE

Il Nuovo Cimento (1943-1954)

ISSUE

8

VOLUME

9

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02782239

DOI

http://dx.doi.org/10.1007/bf02782239

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1009300447


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