Fourier transform, quantum mechanics and quantum field theory on the manifold of general relativity
School of Physics, Tel Aviv University, 69978, Ramat Aviv, Israel
2 Department of Physics, Bar Ilan University, 52900, Ramat Gan, Israel
3 Department of Physics, Ariel University, 40700, Ariel, Israel
Accepted: 12 May 2020
Published online: 8 June 2020
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.
© The Author(s) 2020
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