A perturbative renormalization group approach to light-front Hamiltonian

TL;DR

This paper develops a perturbative renormalization group method for light-front Hamiltonians and applies it to a $ ext{phi}^4$ model, deriving RG equations and analyzing symmetry breaking.

Contribution

It introduces a novel RG scheme for light-front Hamiltonians based on the Bloch-Horowitz approach, applicable to models with spontaneous symmetry breaking.

Findings

RG equations derived at one-loop order match covariant perturbation theory.

Initial cutoff Hamiltonians are constructed for symmetric and broken phases.

The effective potential minimum is identified on the renormalization trajectory.

Abstract

A perturbative renormalization group (RG) scheme for light-front Hamiltonian is formulated on the basis of the Bloch-Horowitz effective Hamiltonian, and applied to the simplest $\phi^4$ model with spontaneous breaking of the $Z_2$ symmetry. RG equations are derived at one-loop order for both symmetric and broken phases. The equations are consistent with those calculated in the covariant perturbation theory. For the symmetric phase, an initial cutoff Hamiltonian in the RG procedure is made by excluding the zero mode from the canonical Hamiltonian with an appropriate regularization. An initial cutoff Hamiltonian for the broken phase is constructed by shifting $\phi$ as $\phi \rightarrow\phi-v$ in the initial Hamiltonian for the symmetric phase. The shifted value $v$ is determined on a renormalization trajectory. The minimum of the effective potential occurs on the trajectory.