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Register a new userDirac and the Path Integral
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N. D. Hari Dass
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Through a very careful analysis of Diracs 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 Diracs 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 Feynmans 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 Schrodinger 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}. Diracs 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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