Quantum Theory in the Rigged Hilbert Space-Irreversibility from Causality

Abstract

After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket formalism, allows the choice of asymmetric boundary conditions analogous to the retarded solutions of the Maxwell equations for the radiation arrow of time. This led to irreversibility on the microphysical level as exemplified by decaying states or resonances. Resonances are mathematically represented by Gamow kets, functionals over a space of very well-behaved (Hardy class) vectors, which have been chosen by a boundary condition (outgoing for decaying states). Gamow states have all the properties that one heuristically needs for quasistable states. For them a Golden Rule can be derived from the fundamental probabilities that fulfills the time-asymmetry condition which could not be realized in the Hilbert space.

60 pages, to appear in Irreversibility and Causality in Quatum Theory: Semigroups and Rigged Hilbert Space, Arno Bohm, H.D. Doebner, P. Kielanowski, eds; Vol. 504 Springer Lecture Notes in Physics

References in corpus (3)

• Violation of CPT and Quantum Mechanics in the K0--K0bar System
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• Testing Quantum Mechanics in the Neutral Kaon System

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