We consider a family of fermionic star products generalising the fermionic Moyal product. The parameter space contains polarisations used to define quantum Hilbert spaces in geometric quantisation. For each polarisation, we find a star product of fermionic functions on quantum states and show that the star product of any function on a quantum state remains a quantum state. We establish the associativity of such star products, which yields representations of the fermionic star product algebras on the quantum Hilbert spaces. The family of star products is compatible with both the flat connection on the bundle of fermionic functions and the projectively flat connection on the bundle of Hilbert spaces or the flat connection of the metaplectically corrected bundle over the space of polarisations. Finally, we relate the fermionic star products to the operator formalism.

我们考虑了一个铁离子星形产品家族，这些产品概括了铁离子Moyal产品。参数空间包含用于在几何量化中定义量子希尔伯特空间的极化。对于每个极化，我们找到了处于量子态的费米离子函数的星积，并表明了处于量子态的任何函数的星积仍然是量子态。我们建立了这类恒星产物的缔合性，从而产生了量子希尔伯特空间上的铁离子恒星产物代数的表示。明星产品系列既与费米离子功能束上的平面连接以及希尔伯特空间束上的射影平面连接兼容，也与极化空间上经偏光校正的束的平面连接兼容。最后，