The Feynman problem for the Klein–Gordon equation
Copyright policy )The Feynman problem for the Klein–Gordon equation
We report on the well-posedness of the Feynman problem for the Klein–Gordon equation on asymptotically Minkowski spacetimes. The main result is the invertibility of the Klein–Gordon operator with Feynman conditions at infinite times. Furthermore, the inverse is shown to coincide with the Duistermaat–Hörmander Feynman parametrix modulo smoothing terms.
Second-order hyperbolic equations, Pseudodifferential operators as generalizations of partial differential operators, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum field theory on curved space or space-time backgrounds, Yang-Mills and other gauge theories in quantum field theory, Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc., FOS: Mathematics, asymptotically Minkowski spacetimes, Feynman conditions at infinite times, Duistermaat-Hörmander Feynman parametrix, Spectral Theory (math.SP), Mathematical Physics, Analysis of PDEs (math.AP)
Second-order hyperbolic equations, Pseudodifferential operators as generalizations of partial differential operators, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum field theory on curved space or space-time backgrounds, Yang-Mills and other gauge theories in quantum field theory, Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc., FOS: Mathematics, asymptotically Minkowski spacetimes, Feynman conditions at infinite times, Duistermaat-Hörmander Feynman parametrix, Spectral Theory (math.SP), Mathematical Physics, Analysis of PDEs (math.AP)
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