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Progress of Theoretical Physics Supplement

A Nonperturbative Renormalization Group Procedure for Light-Front Hamiltonian

T. Sugihara, Masanobu Yahiro

Published May 16, 2013• 0 citations
Publisher

Abstract

We propose a non-perturbative renormalization procedure for light-front Hamiltonian. Wilson's renormalization group prescription is applied to λΦ4-model within a light-front Fock space truncated up to three-body state. Renormalized Hamiltonian which preserves low-energy physics for arbitrary renormalization transformations is presented. Renormalization group equations for mass parameter μ2 and coupling constant λ are derived by integrating high invariant mass space and rescaling transverse momenta and fields.

DOI
10.1143/ptp.120.271

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We propose a non-perturbative renormalization procedure for light-front Hamiltonian. Wilson's renormalization group prescription is applied to λΦ4-model within a light-front Fock space truncated up to three-body state. Renormalized Hamiltonian which preserves low-energy physics for arbitrary renormalization transformations is presented. Renormalization group equations for mass parameter μ2 and coupling constant λ are derived by integrating high invariant mass space and rescaling transverse momenta and fields.
We propose a non-perturbative renormalization procedure for light-front Hamiltonian. Wilson's renormalization group prescription is applied to ..1<,64-model within a light-front Fock space truncated up to three-body state. Renormalized Hamiltonian which preserves lowenergy physics for arbitrary renormalization transformations is presented. Renormalization group equations for mass parameter tl and coupling constant A are derived by integrating high invariant mass space and rescaling transverse momenta and fields.
The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential-operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from standard coupled-cluster theory, to obtain form factors and other observables.
The renormalization of the effective field theories (EFTs) in many-body systems is the most pressing and challenging problem in modern nuclear ab initio calculation. For general non-relativistic EFTs, we prove that the renormalization group (RG) invariance can be achieved if and only if all single-particle momenta are regulated with a universal cutoff Λ. For a numerical demonstration, we construct a series of N^{2}LO chiral forces with Λvarying from 250 MeV to 400 MeV. With all low energy constants fixed in two- and three-nucleon systems, we reproduce the experimental binding energies of ^{4}He and ^{16}O nearly independently of Λ. In contrast, all recent nuclear EFT constructions regulate the relative momenta for Galilean invariance, thus inherently break the RG invariance. This explains the unpleasantly strong cutoff-dependences observed in recent ab initio calculations. Our method can also be used to build RG-invariant EFTs with non-perturbative interactions.
The nonperturbative Hamiltonian eigenvalue problem for bound states of a quantum field theory is formulated in terms of Dirac's light-front coordinates and then approximated by the exponential operator technique of the many-body coupled-cluster method. This approximation eliminates any need for the usual approximation of Fock-space truncation. Instead, the exponentiated operator is truncated, and the terms retained are determined by a set of nonlinear integral equations. These equations are solved simultaneously with an effective eigenvalue problem in the valence sector, where the number of constituents is small. Matrix elements can be calculated, with extensions of techniques from many-body coupled-cluster theory, to obtain form factors and other observables.
We investigate the principal chiral model between two and four dimensions by means of a nonperturbative Wilson-like renormalization-group equation. We are thus able to follow the evolution of the effective coupling constants within this whole range of dimensions without having recourse to any kind of small parameter expansion. This allows us to identify its three-dimensional critical physics and to solve the long-standing discrepancy between the different perturbative approaches that characterizes the class of models to which the principal chiral model belongs.