Circular operators related to some quantum observables

• Autorzy: Wacław Szymański
• Języki publikacji: EN

Abstrakty

EN

Circular operators related to the operator of multiplication by a homomorphism of a locally compact abelian group and its restrictions are completely characterized. As particular cases descriptions of circular operators related to various quantum observables are given.

Słowa kluczowe

EN

circular operator; canonical commutation relation

Kategorie tematyczne

• 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis
• 47B25: Symmetric and selfadjoint operators (unbounded)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 66
• Numer: 1
• Strony: 253-261

Daty

wydano

1997

otrzymano

1995-05-25

Twórcy

autor

Wacław Szymański

• Department of Mathematics, West Chester University, West Chester, Pennsylvania 19383, U.S.A.

Bibliografia

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• [Ha] P. R. Halmos, Measure Theory, Van Nostrand, 1964.
• [Ho] A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, 1982.
• [I] E. K. Infantis, Abstract formulation of the quantum mechanical oscillator phase problem, J. Math. Phys. 12 (1971), 1021-1026.
• [M1] W. Mlak, Notes on quantum circular operators, Institute of Mathematics, Polish Academy of Sciences, preprint 303, 1984.
• [M2] W. Mlak, Notes on circular operators I, II, III, IV, Univ. Iagel. Acta Math. 29 (1992), 145-180.
• [MS] W. Mlak and M. Słociński, Quantum phase and circular operators, Univ. Iagel. Acta Math., 133-144.