Where can I find a covariant approach to Poisson brackets?

In summary, when searching for a detailed discussion on relativistic Poisson brackets, it is important to consider the concepts of covariant phase space and Peierls bracket. These approaches do not require a special time coordinate and are therefore more suitable for relativistic fields and particles. Some recommended resources for further study include the book "QFT" by DeWitt and the articles "Covariant Phase Space" by Larsson and "Covariant Poisson Brackets" by Marsden et al.
  • #1
luxxio
44
0
i am searching for a detailed discussion on the relativistic poisson brackets. where i can found it?
 
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  • #2
See about Pierls bracket. For example, see the book on QFT by DeWitt.
 
  • #3
Why should the Poisson bracket be different for relativistic and non-relativistic fields/particles?
 
  • #4
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.
 
  • #5
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.
 
  • #6
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Related to Where can I find a covariant approach to Poisson brackets?

What is the definition of relativistic Poisson brackets?

Relativistic Poisson brackets are mathematical operators used in classical mechanics to express the equations of motion for relativistic systems. They are derived from the non-relativistic Poisson brackets and take into account the effects of special relativity.

How are relativistic Poisson brackets different from non-relativistic Poisson brackets?

Relativistic Poisson brackets incorporate the principles of special relativity, such as the constancy of the speed of light, into the equations of motion. Non-relativistic Poisson brackets do not take these principles into account and are only valid for systems with low speeds compared to the speed of light.

What are the applications of relativistic Poisson brackets?

Relativistic Poisson brackets are used in theoretical physics to study the behavior of relativistic systems, such as particles moving at high speeds. They are also used in cosmology to model the dynamics of the universe.

How are relativistic Poisson brackets derived?

Relativistic Poisson brackets are derived using the principles of special relativity and Hamiltonian mechanics. They are based on the non-relativistic Poisson brackets and are modified to account for relativistic effects such as time dilation and Lorentz transformations.

What are the limitations of relativistic Poisson brackets?

Relativistic Poisson brackets are only applicable to classical systems and cannot be used to describe quantum systems. They also have limited applicability in extreme conditions, such as near the event horizon of a black hole, where the effects of general relativity must be taken into account.

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