Renormalization of overlapping transverse divergences in a model light-front Hamiltonian

Journal Article · Sat May 15 00:00:00 EDT 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.4657· OSTI ID:6645168

Glazek, S D; Wilson, K G ^[1]

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1. Department of Physics, Ohio State University, Columbus, Ohio 43210 (United States)

We construct a simplified model of a light-front Hamiltonian and describe its renormalization. Our construction starts from a Hamiltonian which acts in a space spanned by free states of two fermions and states of two fermions and one scalar boson. For the purpose of this paper the starting Hamiltonian is regularized by chopping factors in the interaction vertices. We derive an effective Hamiltonian acting in the space of two fermions. Then we make [ital ad] [ital ho]c simplifications in the effective Hamiltonian to produce a model that we can analyze. We drop fermion self-interactions and replace the eigenvalue in the effective one-boson-exchange term by a constant. Our model Hamiltonian acts in the space of two fermions only. The model involves logarithmic ultraviolet transverse divergences, analogous to overlapping divergences in perturbative Lagrangian [ital S]-matrix calculations. We describe the construction of a Hamiltonian counterterm that removes the divergences to all orders in Hamiltonian perturbation theory. The counterterm is local in the transverse direction and contains an arbitrary function of the longitudinal momenta of fermions. We suggest that a suitable choice of the arbitrary function may partly remove the violation of rotational invariance in the spectrum of the model Hamiltonian. The renormalization group transformation for the renormalized two-fermion interaction, [ital V][sub [lambda]], is determined by a nonlinear integro-differential equation of the form [ital dV][sub [lambda]]/[ital d][lambda]=[minus][ital V][sub [lambda]][ital K[lambda]][ital V[lambda]], where [ital K][sub [lambda]] is a known kernel and [lambda] is the scale of the relative transverse momenta of fermions at which the interactions are chopped off.

• OSTI ID: 6645168
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 47:10; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662230* -- Quantum Chromodynamics-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
GLUONS
HADRONS
INTERACTIONS
LIGHT CONE
MESONS
PARTICLE INTERACTIONS
POSTULATED PARTICLES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK-ANTIQUARK INTERACTIONS
RENORMALIZATION
SPACE-TIME
VECTOR MESONS