BRST Hamiltonian quantization of a spinless particle in a curved background

The BRST (Becchi-Rouet-Stora-Tyutin) Hamiltonian formalism is employed to quantize a spinless particle in the background of an arbitrary gravitational field. The gauge-fixed Hamiltonian action is obtained in the extended phase space including the ghosts. The partition function is obtained in the phase-space path-integral representation. The second-quantized action is presented in an elegant manner following Siegel’s technique.