(Q6927583)

English

Moyal product

associative, non-commutative product on the functions on ℝ²ⁿ

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f\star g=m\circ \exp \left({\frac {1}{2}}\mathrm {i} \hbar \Pi ^{ij}\partial _{i}\partial _{j}\right)(f\otimes g)=fg+{\frac {1}{2}}\mathrm {i} \hbar \Pi ^{ij}(\partial _{i}f)(\partial _{j}g)-{\frac {1}{8}}\hbar ^{2}\Pi ^{ij}\Pi ^{km}(\partial _{i}\partial _{k}f)(\partial _{j}\partial _{m}g)+\dotsb

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\star

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\Pi ^{ij}

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