Renormalized Path Integral in Quantum Mechanics

Abstract

We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description requires a modification to the Wiener measure on continuous paths that describes an unusual diffusion process wherein colliding particles occasionally stick together for a random interval of time before going their separate ways.

13 pgs, plain TEX file

References in corpus (5)

• Renormalization in Quantum Mechanics
• Perturbative Renormalization in Quantum Mechanics
• Perturbative Bosonic End Anyon Spectra and Contact Interactions
• Perturbative Renormalizations of Anyon Quantum Mechanics
• Solitons in a Bilocal Field Theory

Cited by in corpus (6)

• Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. II: Rotational Invariance
• Transfer Matrix Formulation of Scattering Theory in Two and Three Dimensions
• Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects
• Renormalized Contact Potential in Two Dimensions
• Exact Solution of the Two-Dimensional Scattering Problem for a Class of $\delta$-Function Potentials Supported on Subsets of a Line
• Scattering by a collection of $\delta$-function point and parallel line defects in two dimensions