Publication details

PT-Symmetry in (Generalized) Effect Algebras



Year of publication 2011
Type Article in Periodical
Magazine / Source International Journal of Theoretical Physics
MU Faculty or unit

Faculty of Science

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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