A Note on the Extrinsic Phase Space Path Integral Method for Quantization on Riemannian Manifold Particle Motions — An Application of the Nash Embedding Theorem
Path integral formulation based on the canonical method is discussed. The Hamilton Jacobi function for regular Lagrangian is obtained using separation of variables method. This function is used to quantize regular systems using path integral method. The path integral is obtained as integration over the canonical phase space coordinates. One illustrative example is considered to demonstrate the application of our formalism.
Path Integral Quantization of Regular Lagrangian