Running Couplings in Hamiltonians

TL;DR

This paper discusses a perturbative similarity renormalization group method for Hamiltonians, illustrating its application to scalar field theory and QCD, providing insights into asymptotic freedom and effective equations for bound states.

Contribution

It introduces a Hamiltonian-based renormalization group procedure with third-order examples, linking asymptotic freedom to effective Hamiltonian formulations.

Findings

Insights into asymptotic freedom in Hamiltonian formalism

Method for ultraviolet-finite effective Schrödinger equations

Invariant dynamics under boosts for bound state analysis

Abstract

We describe key elements of the perturbative similarity renormalization group procedure for Hamiltonians using two, third-order examples: phi^3 interaction term in the Hamiltonian of scalar field theory in 6 dimensions and triple-gluon vertex counterterm in the Hamiltonian of QCD in 4 dimensions. These examples provide insight into asymptotic freedom in Hamiltonian approach to quantum field theory. The renormalization group procedure also suggests how one may obtain ultraviolet-finite effective Schr\"odinger equations that correspond to the asymptotically free theories, including transition from quark and gluon to hadronic degrees of freedom in case of strong interactions. The dynamics is invariant under boosts and allows simultaneous analysis of bound state structure in the rest and infinite momentum frames.