Poincare- and gauge-invariant two-dimensional quantum chromodynamics

Journal Article · Sun Jan 15 00:00:00 EST 1978 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.17.537· OSTI ID:5033214

Bars, I; Green, M B

We present a canonical formulation of two-dimensional quantum chromodynamics in the axial or Coulomb gauge A/sup a//sub 1/ = 0. For consistency with the Lagrange equations of motion, the Hamiltonian must include a nontrivial dynamical background electric field term. This breaks translation invariance inthe gauge-noninvariant sector. We argue, however, that for the purpose of calculating gauge-invariant physical quantities one can consider the naive theory defined by the Feynman rules without the background electric field. We show that the naive theory has an anomalous Poincare algebra due to its non-Abelian character; the theory is Lorentz invariant only in the color-singlet sector. Because of this fact the quark propagator has a noncovariant pole, and the iepsilon prescription is different from the naive one. In the N ..-->.. infinity limit (where N is the number of colors) we can set up a two-component Bethe-Salpeter equation in the color-singlet sector to determine the spectrum of the theory. The resulting equation has an obvious interpretation in terms of forward- and backward-moving strings, and leads to the same spectrum of bound states as that obtained by 't Hooft in the light-cone gauge.

• Research Organization: Department of Physics, Yale University, New Haven, Connecticut 06520
• OSTI ID: 5033214
• Journal Information: Phys. Rev., D; (United States), Vol. 17:2
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM CHROMODYNAMICS
GAUGE INVARIANCE
POINCARE GROUPS
BETHE-SALPETER EQUATION
BOUND STATE
COLOR MODEL
COULOMB FIELD
EIGENSTATES
EQUATIONS OF MOTION
FEYNMAN DIAGRAM
HAMILTONIANS
LAGRANGIAN FUNCTION
LIGHT CONE
PROPAGATOR
RENORMALIZATION
COMPOSITE MODELS
DIAGRAMS
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
EQUATIONS
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
PARTICLE MODELS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUARK MODEL
SPACE-TIME
SYMMETRY GROUPS
645400* - High Energy Physics- Field Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics