Time Asymmetric Quantum Theory - I Modifying an Axiom of Quantum Physics

Details Time Asymmetric Quantum Theory - I Modifying an Axiom of Quantum Physics Time Asymmetric Quantum Theory - I Modifying an Axiom of Quantum Physics

2002-12-22

arxiv.org/abs/quant-ph/0212130v2

Fortsch.Phys. 51 (2003) 551-568

Physics

Quantum Physics

23 pages

Scientific paper

10.1002/prop.200310073

A slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of scattering theory) and the space of observables (out-``states'' of scattering theory) the new axiom associates states and observables to two different Hardy subspaces which are dense in the same Hilbert space and analytic in the lower and upper complex energy plane, respectively. As a consequence of this new axiom the dynamical equations (Schr\"{o}dinger or Heisenberg) integrate to a semigroup evolution. Extending this new Hardy space axiom to a relativistic theory provides a relativistic theory of resonance scattering and decay with Born probablilities that fulfill Einstein causality and the exponential decay law.

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