PROBABILITY-CONSERVING TRANSFORMATIONS AND SUPERSELECTION RULES IN QUANTUM THEORY

Journal Article · Thu Oct 31 23:00:00 EST 1963 · Annals of Physics (New York) (U.S.)

DOI:https://doi.org/10.1016/0003-4916(63)90351-8· OSTI ID:4124546

O'Raifeartaigh, L; Rasche, G

A theorem due to Wigner, which states that any transformation of a Hilbert space that preserves the absolute value of the inner products is equivalent to either a unitary or anti-unitary transformation, is considered. It is pointed out that two previous proofs of the theorem are not complete, and a new proof of the theorem, considered purely from the mathematical point of view, is given. The physical meanding of the theorem, and its connection with invariances and symmetries of physical systems, is then discussed. Particular attention is paid to the case in which superselection rales are present. A second proof of the theorem is given. (auth)

• Research Organization: Dublin Inst. for Advanced Studies
• NSA Number: NSA-18-004477
• OSTI ID: 4124546
• Journal Information: Annals of Physics (New York) (U.S.), Journal Name: Annals of Physics (New York) (U.S.) Vol. Vol: 25; ISSN APNYA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

FIELD THEORY
HILBERT SPACE
INVARIANCE PRINCIPLE
MATHEMATICS
PHYSICS
PROBABILITY
QUANTUM MECHANICS
STATISTICS
SUPERSELECTION RULES
SYMMETRY
TRANSIENTS