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A pair of curved curly braces around two functions in classical mechanics.
Also known as: Poisson brackets, Classical bracket, Braces in mechanics
The Poisson bracket is the classical ancestor of the quantum commutator: it takes two functions on phase space and returns a third, and it generates time evolution. Dirac's insight was that replacing it by a commutator divided by iℏ turns classical mechanics into quantum mechanics.
Denotes the Poisson bracket of two functions on phase space, built from their position and momentum derivatives.
Contexts: Mathematics
Generates time evolution in Hamiltonian mechanics: a quantity's rate of change is its bracket with the Hamiltonian.
Contexts: Mathematics
Corresponds to the quantum commutator divided by iℏ, which is the formal bridge Dirac used to build canonical quantisation.
Contexts: Mathematics
A pair of curly braces, each a curved stroke pinched to a central point, enclosing two function names separated by a comma.