Star product representation of coherent state path integrals

In this paper, we determine the star product representation of coherent path integrals. By employing the properties of generalized delta functions with complex arguments, the Glauber–Sudarshan P-function corresponding to a non-diagonal density operator is obtained. Then, we compute the Husimi–Kano Q-representation of the time evolution operator in terms of the normal star product. Finally, the optical equivalence theorem allows us to express the coherent state path integral as a star exponential of the Hamiltonian function for the normal product.