Hendry M. Lim
We present the explicit form of the "hatted star product" within the Cahill-Glauber correspondence framework, which is a commutative mapping of two Hilbert space operators that encodes the quantization prescription. It serves as the structural mirror to the star product, which encodes the noncommutative nature of quantum mechanics in phase space.
This paper contains 9 sections, 1 theorem, 67 equations.
Theorem 1
Let $f=f\left(\alpha,\alpha^*\right)$ and $g=g\left(\alpha,\alpha^*\right)$ be Schwartz functions of the complex phase space variable $\alpha$ and its formally-independent complex conjugate $\alpha^*$. Let $\hat{a}$ and $\hat{a}^\dagger$ be the quantization of $\alpha$ and $\alpha^*$, respectively. where, with the formal operator derivatives defined in Eq. eq:oper_derivatives, the binary map is
