= Moyal product
{wiki=Moyal_product}
The Moyal product is a mathematical operation used in the framework of phase space formulation of quantum mechanics, particularly in the context of deformation quantization. It allows one to define a product of functions on phase space that encapsulates the non-commutativity of quantum mechanics in a way that is analogous to the multiplication of classical observables. In classical mechanics, the observable quantities are usually functions on phase space, and the product of two observables is simply their pointwise product.
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