Special example of relativistic Hamiltonian field theory

Journal Article · Fri May 15 04:00:00 EDT 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.45.3740· OSTI ID:7287433

Glazek, S D; Perry, R J ^[1]

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

We study fermion-boson bound and scattering states in a (3+1)-dimensional Yukawa theory, using a Tamm-Dancoff truncation of light-front field theory. We retain only two sectors of Fock space, the sector with one fermion and the sector with one fermion and one boson. Such truncations violate Lorentz covariance if one employs the canonical Hamiltonian. In order to restore covariance we modify the Hamiltonian, introducing new terms and allowing all terms to depend on the Fock-space sectors within which or between which they act. In this special example, which is closely related to the Lee model, simple sector-dependent mass and vertex counterterms are sufficient to yield finite observables that are exactly covariant for states whose invariant mass is less than a critical value determined by the cutoffs. Triviality prevents the complete removal of cutoffs from the Hamiltonian that we consider. This calculation illuminates several basic features of the renormalization program required by the nonperturbative light-front Tamm-Dancoff approach.

• DOE Contract Number: AC02-76ER01545
• OSTI ID: 7287433
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 45:10; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120 -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
662340 -- Hadron Interactions-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
BOUND STATE
FERMIONS
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
HAMILTONIANS
INTERACTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
NUCLEAR POTENTIAL
PARTICLE INTERACTIONS
PERTURBATION THEORY
POTENTIALS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RELATIVITY THEORY
RENORMALIZATION
SCATTERING
SYMMETRY BREAKING
TAMM-DANCOFF METHOD
YUKAWA POTENTIAL