Partial inner product spaces, a unifying language for quantum mechanics
(2012) Geometric Methods in Physics, XXX Workshop, Bialowieza 2011 — Location: Bialowieza (26.June.2011)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- In order to obtain a rigorous version of the Dirac formulation of quantum mechanics, one has to go beyond Hilbert space and one usually resorts to a Rigged Hilbert space (RHS). However, this is a particular case of partial inner product spaces (PIP spaces), a general formalism that also generalizes many families of function spaces that play a central role in analysis. In this paper, we shall give an overview of PIP spaces and operators on them, defined globally. We will also discuss a number of operator classes, such as morphisms and projections.
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Citations
Antoine, J.-P. (2012). Partial inner product spaces, a unifying language for quantum mechanics. In P. Kielanowski, S.T. Ali, A. Odzijewicz, M. Schlichenmaier, and T. Voronov (eds.) (ed.), Geometric Methods in Physics, XXX Workshop, Bialowieza 2011 (p. p. 157-164). Springer. https://hdl.handle.net/2078.5/26243