Electronic Resource
Springer
Communications in mathematical physics
8 (1968), S. 132-146
ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract A non-commutative version of probability theory is outlined, based on the concept of aΣ*-algebra of operators (sequentially weakly closedC*-algebra of operators). Using the theory ofΣ*-algebras, we relate theC*-algebra approach to quantum mechanics as developed byKadison with the probabilistic approach to quantum mechanics as axiomatized byMackey. TheΣ*-algebra approach to quantum mechanics includes the case of classical statistical mechanics; this important case is excluded by theW*-algebra approach. By considering theΣ*-algebra, rather than the von Neumann algebra, generated by the givenC*-algebraA in its reduced atomic representation, we show that a difficulty encountered byGuenin concerning the domain of a state can be resolved.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01645801
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