Renormalized nonperturbative fermion model in Covariant Light Front Dynamics

Abstract

Within the framework of the covariant formulation of Light-Front Dynamics, we develop a nonperturbative renormalization scheme in the fermion model supposing that the composite fermion is a superposition of the "bare" fermion and a fermion+boson state. We first assume the constituent boson to be spinless. Then we address the case of gauge bosons in the Feynman and in the Light-Cone gauges. For all these cases the fermion state vector and the necessary renormalization counterterms are calculated analytically. It turns out that in Light-Front Dynamics, to restore the rotational invariance, an extra counterterm is needed, having no any analogue in Feynman approach. For gauge bosons the results obtained in the two gauges are compared with each other. In general, the number of spin components of the two-body (fermion+boson) wave function depends on the gauge. But due to the two-body Fock space truncation, only one non-zero component survives for each gauge. And moreover, the whole solutions for the state vector, found for the Feynman and Light-Cone gauges, are the same (except for the normalization factor). The counterterms are however different

44 pages, 12 figures, to be publisehd in Physical Review D

References in corpus (9)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Explicitly Covariant Light-Front Dynamics and Relativistic Few-Body Systems
• Pauli--Villars as a Nonperturbative Ultraviolet Regulator in Discretized Light-Cone Quantization
• Application of Pauli-Villars Regularization and Discretized Light-Cone Quantization to a (3+1)-Dimensional Model
• Application of Pauli-Villars regularization and discretized light-cone quantization to a single-fermion truncation of Yukawa theory
• The mass renormalization of nonperturbative light-front Hamiltonian theory: An illustration using truncated, Pauli-Villars-regulated Yukawa interactions
• Nonperturbative renormalization in a scalar model within Light-Front Dynamics
• Perturbative Tamm-Dancoff Renormalization
• The charge and mass perturbative renormalization in explicitly covariant LFD

Cited by in corpus (14)

• Systematic renormalization scheme in light-front dynamics with Fock space truncation
• Nonperturbative light-front Hamiltonian methods
• A nonperturbative calculation of the electron's magnetic moment
• Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model
• Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space
• Many-body Fock sectors in Wick-Cutkosky model
• Regularization of fermion self-energy and electromagnetic vertex in Yukawa model within light-front dynamics
• Taylor-Lagrange renormalization scheme. Application to light-front dynamics
• Nonperturbative solution of scalar Yukawa model in two- and three-body Fock space truncations
• Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics
• Nonperturbative renormalization in light-front dynamics and applications
• Quarkonium wave functions on the light front
• Non-perturbative renormalization in Light Front Dynamics with Fock space truncation
• Nonperturbative calculations in truncated Fock space in LFD