2001/04/01 by Hanno Gottschalk, H. Gottschalk · 4 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Counterexample #Discrete mathematics #Field (mathematics) #Geometry and complex manifolds #Law #Mathematical physics #Mathematics #Metric (unit) #Physics #Pure mathematics #Quantum #Quantum field theory #Quantum mechanics #Space (punctuation) #Stability (learning theory) #State (computer science) #Statement (logic) #advanced mathematical theories #math-ph #math.MP #msc:81T05
paper · pdf · doi:10.1016/s0034-4877(01)80039-2
published in Reports on Mathematical Physics 47(2), 241-246 (Elsevier BV)
openalex publication_date 2001/04/01 · arxiv created 2004/08/25 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We prove that for a Wightman quantum field ϕ(x) the assumptions (i) positivity of the metric on the state space \cal H of the theory (ii) the asymptotic condition in the form of Yang-Feldman equations and (iii) Klein-Gordon equation for the outgoing field imply that the states generated by application of the asymptotic fields to the vacuum are stable. We prove by a counter example that this statement is wrong in the case of quantum fields with indefinite metric.