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Analytical Mechanics for Relativity and Quantum Mechanics$
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Oliver Johns

Print publication date: 2011

Print ISBN-13: 9780191001628

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780191001628.001.0001

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Generating Functions

Generating Functions

Chapter:
(p.451) 20 Generating Functions
Source:
Analytical Mechanics for Relativity and Quantum Mechanics
Author(s):

Oliver Davis Johns

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780191001628.003.0020

This chapter proposes methods for creating transformations that will automatically be canonical. Canonical transformations can be created by first choosing what are called generating functions. Using one of these generating functions in the formalism to be described will generate a transformation that will be canonical by construction. The generating functions can be quite general, leading to a wide selection of possible canonical transformations. Not only does every generating function lead to a canonical transformation, the converse is also true. Given any canonical transformation, a generating function can always be found that will generate it. The chapter begins by first relating canonical transformations to the existence of an intermediate function that will be called a protogenerating function.

Keywords:   generating functions, formalism, canonical transformations, intermediate function, protogenerating function

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