Where can I find a covariant approach to Poisson brackets?

luxxio
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i am searching for a detailed discussion on the relativistic poisson brackets. where i can found it?
 
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See about Pierls bracket. For example, see the book on QFT by DeWitt.
 
Why should the Poisson bracket be different for relativistic and non-relativistic fields/particles?
 
crackjack said:
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.
 
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.
 
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Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
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