2002/12/31 by A. Bohm, A.R. Bohm, M. Loewe +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Axiom #Causality (physics) #Constructive set theory #Hilbert space #Noncommutative and Quantum Gravity Theories #Observable #POVM #Quantum #Quantum Mechanics and Applications #Rigged Hilbert space #Scattering theory #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1002/prop.200310073
published as Fortsch.Phys.51:551-568,2003 · 23 pages
arxiv created 2003/02/14 · openalex publication_date 2003/05/13 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.