ArticleOriginal scientific text

Title

Circular operators related to some quantum observables

Authors 1

Affiliations

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

Abstract

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.

Keywords

circular operator, canonical commutation relation

Bibliography

  1. [AHHK] W. Arveson, D. Hadwin, T. B. Hoover and E. Kymala, Circular operators, Indiana Univ. Math. J. 33 (1984), 583-595.
  2. [D] J. Dixmier, Von Neumann Algebras, North-Holland, 1981.
  3. [Ha] P. R. Halmos, Measure Theory, Van Nostrand, 1964.
  4. [Ho] A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, 1982.
  5. [I] E. K. Infantis, Abstract formulation of the quantum mechanical oscillator phase problem, J. Math. Phys. 12 (1971), 1021-1026.
  6. [M1] W. Mlak, Notes on quantum circular operators, Institute of Mathematics, Polish Academy of Sciences, preprint 303, 1984.
  7. [M2] W. Mlak, Notes on circular operators I, II, III, IV, Univ. Iagel. Acta Math. 29 (1992), 145-180.
  8. [MS] W. Mlak and M. Słociński, Quantum phase and circular operators, Univ. Iagel. Acta Math., 133-144.
Pages:
253-261
Main language of publication
English
Received
1995-05-25
Published
1997
Exact and natural sciences