Bouquet Of Numbers And Other Scientific Offerings, A by Bernstein Jeremy

Author:Bernstein, Jeremy
Language: eng
Format: epub
ISBN: 9789814759793
Publisher: World Scientific Publishing Company
Published: 2016-04-30T04:00:00+00:00

Here L is the Lagrangian and what one has in the exponent is the quantum version of the classical action.

This leaves the reader absolutely baffled at to what “corresponds to” means. Feynman converted this into an equation with a factor in front which he found by doing examples. He later asked Dirac if he had ever worked out this factor and Dirac said no. It is not clear what this integral means. It becomes clearer if you break up the transition from one time to the other into small steps. In the Feynman version these steps are called “paths” and the integral is a sum over all paths consistent with the constraints on the system. In some simple cases such as the free particle or the harmonic oscillator this path integral can be carried out. Dirac observed that if you go to the limit of a vanishing Planck’s constant the only path that matters is the classical one. In this way the classical world is re-discovered.

Schwinger’s starting point is also the transition amplitude. Indeed it is the differential form of Dirac’s action integral, namely

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