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luxxio
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i am searching for a detailed discussion on the relativistic poisson brackets. where i can found it?
Poisson brackets require a choice of a special time coordinate, so they are not relativistic covariant.crackjack said:Why should the Poisson bracket be different for relativistic and non-relativistic fields/particles?
Demystifier said:Poisson brackets require a choice of a special time coordinate, so they are not relativistic covariant.
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.
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.
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.
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.
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.