Moyal product

The Moyal product is a mathematical tool used in quantum mechanics to combine functions in phase space, which represents all possible positions and momenta of a system. Unlike classical multiplication, the Moyal product accounts for quantum effects by introducing a special correction that captures the uncertainty and wave-like nature of particles. It allows physicists to work with quantum states in a way that resembles classical physics but incorporates essential quantum properties, providing a bridge between the classical and quantum descriptions of physical systems.