Covariant poisson brackets for classical fields

✍ Scribed by J.E Marsden; R Montgomery; P.J Morrison; W.B Thompson

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 941 KB
• Volume: 169
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(86)90157-0

✦ Synopsis

Poisson brackets that are spacetime covariant are presented for a variety of relativistic field theories. These theories include electromagnetism, general relativity, and general relativistic fluids and plasmas in Eulerian representation. The examples presented suggest the development of a general theory; the beginnings of such a theory are presented. Our covariant bracket formalism provides a general setting for. amongst other things, clarifying the transition from the covariant formalism to the dynamical 3 + 1 Hamiltonian formalism of Dirac and Arnowitt, Deser, and Misner. We illustrate the relevant procedures with electromagnetism.

4? 1986 Academic Press. Inc.

A. Purefields, typified by gauge fields, where F and S in (1.1) are functions of the basic field variables 4" and their conjugate momenta ~5.