 Next to the sine bracket discussed, Groenewold further introduced the cosine bracket, elaborated by Baker,
Here, again, ★ is the star-product operator in phase space, and are differentiable phase-space functions, and is the ordinary product.The sine and cosine brackets are, respectively, the results of antisymmetrizing and symmetrizing the star product.Thus, as the sine bracket is the Wigner map of the commutator, the cosine bracket is the Wigner image of the anticommutator in standard quantum mechanics.