Dirac and the Path Integral

• URL: http://arxiv.org/abs/2003.12683v1
• Date: Sat, 28 Mar 2020 01:52:59 GMT
• Title: Dirac and the Path Integral
• Authors: N. D. Hari Dass
• Abstract summary: I show that Dirac's contributions to the birth of the path-integral approach to quantum mechanics is not restricted to his seminal demonstration of how Lagrangians appear naturally in quantum mechanics. I call Dirac's path-integral it Dirac path-integral which is far more general than Feynman's while possessing all its desirable features.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Through a very careful analysis of Dirac's 1932 paper on the Lagrangian in Quantum Mechanics as well as the second and third editions of his classic book {\it The Principles of Quantum Mechanics}, I show that Dirac's contributions to the birth of the path-integral approach to quantum mechanics is not restricted to just his seminal demonstration of how Lagrangians appear naturally in quantum mechanics, but that Dirac should be credited for creating a path-integral which I call {\it Dirac path-integral} which is far more general than Feynman's while possessing all its desirable features. On top of it, the Dirac path-integral is fully compatible with the inevitable quantisation ambiguities, while the Feynman path-integral can never have that full consistency. In particular, I show that the claim by Feynman that for infinitesimal time intervals, what Dirac thought were analogues were actually proportional can not be correct always. I have also shown the conection between Dirac path-integrals and the Schr\"odinger equation. In particular, it is shown that each choice of Dirac path-integral yields a {\it quantum Hamiltonian} that is generically different from what the Feynman path-integral gives, and that all of them have the same {\it classical analogue}. Dirac's method of demonstrating the least action principle for classical mechanics generalizes in a most straightforward way to all the generalized path-integrals.

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