Renormalization Group in Quantum Mechanics

TL;DR

This paper introduces the concept of running coupling constants in quantum mechanics, using renormalization group equations to analyze their evolution, with examples like the harmonic oscillator and curved space propagation.

Contribution

It develops a framework for applying renormalization group methods to quantum mechanics, deriving scaling relations and constructing low energy effective models.

Findings

Derived Hamiltonian and Lagrangian scaling relations.

Presented evolution equations for coupling constants.

Constructed low energy effective models.

Abstract

The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The hamiltonian and the lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models.