Renormalization Group in Quantum Mechanics

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.

Updated and extended version to appear in Annals of Physics, 24pg, TEX file

References in corpus (2)

• Renormalization in 1D Quantum Mechanics: contact interactions
• On the Hamiltonian Approach and Path Integration for a Point Particle Minimally Coupled to Electromagnetism

Cited by in corpus (15)

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• Lectures on renormalization and asymptotic safety
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• Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics. I. General Theory
• One-Loop Quantum Effects in Carroll Scalars
• Effective dynamics of a classical point charge
• Anti-Ferromagnetic Condensate in Yang-Mills Theory
• Renormalisation in Quantum Mechanics
• Quantum Mechanics in the Infrared
• The Ultraviolet Structure of Quantum Field Theories. Part 1: Quantum Mechanics
• Inflationary Potentials from the Exact Renormalisation Group
• Renormalization in 1D Quantum Mechanics: contact interactions
• Time scale of stationary decoherence
• Low energy properties of non-perturbative quantum systems: a space reduction approach
• A Short Lecture on Divergences