Hamiltonian Path Integrals In Momentum Space Representation via White Noise Techniques
Wolfgang Bock
TL;DR
This paper employs white noise analysis to rigorously construct Feynman integrals for the harmonic oscillator in momentum space, demonstrating momentum conservation in the free case within a distributional framework.
Contribution
It introduces a white noise approach to define Feynman integrals in momentum space, providing a rigorous mathematical foundation for quantum harmonic oscillators.
Findings
Constructed Feynman integrand as a Hida distribution
Proved momentum conservation in the free potential limit
Applied white noise techniques to quantum mechanics
Abstract
The concepts of Feynman integrals in white noise analysis are used to construct the Feynman integrand for the harmonic oscillator in momentum space representation as a Hida distribution. Moreover it is shown that in a limit sense, the potential free case fulfills the conservation of momentum.
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