The dynamical evolution in quantum physics and its semi-group

Arno Bohm ()
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Arno Bohm: University of Texas at Austin, Department of Physics

A chapter in Physical and Mathematical Aspects of Symmetries, 2017, pp 27-40 from Springer

Abstract: Abstract Experiments on quantum systems are usually divided into preparation of states and the registration of observables. Using the traditional mathematical methods (the Hilbert space or the Schwartz space of distribution theory), it is not possible to distinguish mathematically between observables and states. The Hilbert space boundary conditions for the dynamical equation lead by mathematical theorems (Stone-von-Neumann) to unitary group evolution with –∞ ˂ t ˂ +. In contrast, the set-up of a scattering experiments calls for time-asymmetric boundary conditions. Therefore, a new axiom of quantum theory is needed. This is the Hardy space axiom, which uses a pair of Hardy spaces, one of them for states (defined by the experimental preparation procedure), and the other for observables (defined by detectors). The Paley-Wiener theorem for Hardy spaces then leads to semi-groups and time asymmetry. It introduces a finite beginning of time t 0 for a time asymmetric quantum theory, which can be observed by an ensemble of onset times t 0 (i) of dark periods in Dehmelt’s quantum jump experiments with single ions [1].

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-69164-0_5

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DOI: 10.1007/978-3-319-69164-0_5

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