CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE


Dereli T. T. , Tegmen A., Hakioglu T.

INTERNATIONAL JOURNAL OF MODERN PHYSICS A, vol.24, pp.4769-4788, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24
  • Publication Date: 2009
  • Doi Number: 10.1142/s0217751x09044760
  • Title of Journal : INTERNATIONAL JOURNAL OF MODERN PHYSICS A
  • Page Numbers: pp.4769-4788

Abstract

Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.