Deformations, Quantizations, and Noncommutativity
نویسنده
چکیده
Definition 1.1. A Poisson algebra is an associative algebra A over a field K (fixed, of characteristic zero), equipped with a Lie bracket {−,−} such that {x,−} is a derivation for any x ∈ A, i.e. {x, yz} = {x, y}z + y{x, z}. Definition 1.2. A Poisson structure on a manifold M is a Poisson bracket {−,−} on the algebra C∞(M). Example 1.3. On T ∗Rn with position coordinates q1, ..., qn and momentum coordinates p1, ..., pn, the standard bracket is given by
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