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

Abstract

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 (Schrödinger 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.

23 pages

References in corpus (3)

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• Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics
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Cited by in corpus (9)

• Resonance expansions in quantum mechanics
• Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution
• Spherical harmonics and rigged Hilbert spaces
• Dynamics of algebras in quantum unstable systems
• The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I
• The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
• On the inconsistency of the Bohm-Gadella theory with quantum mechanics
• Gamow vectors formalism applied to the Loschmidt echo
• The preparation time in a scattering experiment