Where can I find a covariant approach to Poisson brackets?

[luxxio]

i am searching for a detailed discussion on the relativistic poisson brackets. where i can found it?

 

[Demystifier]

See about Pierls bracket. For example, see the book on QFT by DeWitt.

 

[crackjack]

Why should the Poisson bracket be different for relativistic and non-relativistic fields/particles?

 

[Demystifier]

Why should the Poisson bracket be different for relativistic and non-relativistic fields/particles?

Poisson brackets require a choice of a special time coordinate, so they are not relativistic covariant.

 

[Thomas Larsson]

A Yahoo search for "relativistic Poisson bracket" (it may be picky with correct spelling) yields a single hit: http://landau.rice.edu/~aac/pubs/Phys-Plasmas.pdf

However, a better search phrase is "covariant phase space" which yields ca 142,000 hits on Google. Even better, searching for "covariant phase space"+Larsson yields six hits on Yahoo, all apparently written by a younger myself.

 

[A. Neumaier]

Poisson brackets require a choice of a special time coordinate, so they are not relativistic covariant.

Peierls bracket http://en.wikipedia.org/wiki/Peierls_bracket singles out no time coordinate.

Marsden et al. http://count.ucsc.edu/~rmont/papers/covPBs85.PDF is another interesting covariant approach to Poisson brackets.