Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory

Details Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory

2009-10-07

arxiv.org/abs/0910.1192v1

Acta Polytechnica 50 (2010) 62 - 68

Physics

Mathematical Physics

10 pages, talk, int. conf. "Selected Topics in Mathematical and Particle Physics" (Prague, 5-7 May 2009, http://www.km.fjfi.

Scientific paper

A few recent innovations of applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly broadened four-Hilbert-space update. Among applications involving several new scattering and bound-state problems the central role is played by the models using apparently non-Hermitian ("crypto-Hermitian") Hamiltonians with real spectra. The formalism (originally inspired by the topical need of mathematically consistent description of tobogganic quantum models) is shown to admit certain unusual nonlocal and/or "moving-frame" representations of the standard physical Hilbert space of wave functions.

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