RAPIDLY CONVERGING PATH INTEGRAL FORMALISM .1. QUANTUM-MECHANICS

The action to be used in the path integral formalism is expanded in a systematic way in powers of the time spacing ε{lunate} in order to optimize the convergence to the continuum limit. This modifies and extends the usual formalism in a transparent way. The path integral approximation to the Green function obtained by this method approaches the continuum Green function with a higher power of ε{lunate} than the usual one. The general theoretical derivations are exemplified analytically for the harmonic oscillator and by Monte Carlo methods for the anharmonic oscillator. We also show how curvilinear and curved spaces can naturally be treated within this formalism. Work on field theory is in progress. © 1990.