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EnglishWhen the configuration space of a quantum particle is semibounded, the von Neumann algebra of the observables W(+) is generated by a unitary group {V(beta) = exp(-i beta q)}, beta is an element of R, and a semigroup {U(alpha)}, alpha >= 0, of isometries. We show that when W(+) is a factor it is completely reducible into equivalent components, and that in each component the lower end x(0) of the spectrum of q is the same. We give an algebraic characterization of x(0) and also obtain a straightforward new proof that the irreducible representations of W(+) with the same value of x(0) are equivalent. In the general case W(+) decomposes into the direct integral of factors which correspond to the possible values of x(0).
| Autori interni: | |
| Autori: | Bracci L; Picasso LE |
| Titolo: | On the Reducibility of the Weyl Algebra for a Semibounded Space |
| Anno del prodotto: | 2009 |
| Digital Object Identifier (DOI): | 10.1007/s11005-009-0334-3 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
http://hdl.handle.net/11568/196764
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