Symmetries of quantum systems: a partial inner product space approach
(2008) Journal of Physics A: Mathematical and Theoretical — Vol. 41, n° 30, p. 1-13 (2008)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- We first give a quick survey of the realization of symmetries of quantum systems in the various formalisms of quantum mechanics: traditional (Hilbert space), algebraic (C*-algebras), rigged Hilbert spaces, *-algebras of unbounded operators, partial *-algebras of closable operators. Then we describe in some detail the concept of partial inner product spaces (PIP-spaces) and operators on them. Finally, we examine various classes of operators on PIP-spaces that allow a correct realization of symmetries.
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Citations
Antoine, J.-P. (2008). Symmetries of quantum systems: a partial inner product space approach. Journal of Physics A: Mathematical and Theoretical, 41(30), 1-13. https://doi.org/10.1088/1751-8113/41/30/304037 (Original work published 2008)