2003/01/29 by Paschke, Mario
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.math-ph/0301040
openalex publication_date 2003/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As R.Feynman has shown to F. Dyson -- who published it then in 1990 under the name of "Feynman's proof of Maxwell's equations" -- the only interactions compatible with the canonical uncertainty relation (for scalar particles on flat \R3) are the Lorentz covariant electromagnetic interactions. We generalize Feynman's argument to arbitrary configuration spaces, thereby clarifying its hidden assumptions as well as its geometrical significance. In addition, our result establishes a correspondence between globally hyperbolic spacetimes and solutions to our (algebraically formulated) axioms for nonrelativistic quantum mechanics.