Remarks on the Hamiltonian path integral in polar coordinates

Abstract

Problems associated with the derivation of the Hamiltonian path integral in polar coordinates are examined. First the use of the ill-defined asymptotic formula of the modified Bessel function is pointed out. A procedure is proposed to justify its practical use, in which the mass m is complexified and the limit Imm→0 is taken after path integrations. Hereby a restriction is imposed on the class of allowed potentials. The difference between the Hamiltonian path integral so obtained and the phase space path integral formally defined is also discussed.