2019/07/03 by L. P. Horwitz, Horwitz, L. P. · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #Mathematical Analysis and Transform Methods #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1907.03582
openalex publication_date 2019/07/03 · openalex created_date 2020/04/24 · openalex updated_date 2026/07/28
A proof is given for the Fourier transform for functions in a quantum mechanical Hilbert space on a non-compact manifold in general relativity. In the (configuration space) Newton-Wigner representation we discuss the spectral decomposition of the canonical operators and give a proof of the Parseval-Plancherel relation and the Born rule for linear superposition. We then discuss the representations of pure quantum states and their dual vectors, and construct the Fock space and the associated quantum field theory for Bose-Einstein and Fermi-Dirac statistics.