PT-Symmetry in (Generalized) Effect Algebras
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Theoretical Physics |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.springerlink.com/content/88684020j5t72x12/ |
| Doi | http://dx.doi.org/10.1007/s10773-010-0594-9 |
| Field | General mathematics |
| Keywords | (Generalized) effect algebra; Partially ordered commutative group; Hilbert space; (Unbounded) linear operators; PT-symmetry; Pseudo-Hermitian quantum mechanics |
| Description | We show that an eta (+)-pseudo-Hermitian operator for some metric operator eta (+) of a quantum system described by a Hilbert space H yields an isomorphism between the partially ordered commutative group of linear maps on H and the partially ordered commutative group of linear maps on H(p+). The same applies to the generalized effect algebras of positive operators and to the effect algebras of c-bounded positive operators on the respective Hilbert spaces H and H(p+). Hence, from the standpoint of (generalized) effect algebra theory both representations of our quantum system coincide. |
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