Systematic Renormalization in Hamiltonian Light-Front Field Theory

Abstract

We develop a systematic method for computing a renormalized light-front field theory Hamiltonian that can lead to bound states that rapidly converge in an expansion in free-particle Fock-space sectors. To accomplish this without dropping any Fock sectors from the theory, and to regulate the Hamiltonian, we suppress the matrix elements of the Hamiltonian between free-particle Fock-space states that differ in free mass by more than a cutoff. The cutoff violates a number of physical principles of the theory, and thus the Hamiltonian is not just the canonical Hamiltonian with masses and couplings redefined by renormalization. Instead, the Hamiltonian must be allowed to contain all operators that are consistent with the unviolated physical principles of the theory. We show that if we require the Hamiltonian to produce cutoff-independent physical quantities and we require it to respect the unviolated physical principles of the theory, then its matrix elements are uniquely determined in terms of the fundamental parameters of the theory. This method is designed to be applied to QCD, but for simplicity, we illustrate our method by computing and analyzing second- and third-order matrix elements of the Hamiltonian in massless phi-cubed theory in six dimensions.

47 pages, 6 figures; improved referencing, minor presentation changes

References in corpus (4)

• A Weak-Coupling Treatment of Nonperturbative QCD Dynamics to Heavy Hadrons
• Similarity Renormalization, Hamiltonian Flow Equations, and Dyson's Intermediate Representation
• Effects of Massive Gluons on Quarkonia in Light-Front QCD
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Cited by in corpus (6)

• Nonperturbative light-front Hamiltonian methods
• Glueballs on a transverse lattice
• Glueballs in a Hamiltonian Light-Front Approach to Pure-Glue QCD
• Boost-Invariant Running Couplings in Effective Hamiltonians
• Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization
• Two-Loop Calculations in phi^4 Light-Front Field Theory