Towards solving QCD: The transverse zero modes in light-cone quantization

Journal Article · Sat Jul 15 04:00:00 EDT 1995 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.52.1176· OSTI ID:69565

Pauli, H; Kalloniatis, A C ^[1]; Pinsky, S S ^[2]

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1. Max-Planck-Institut fuer Kernphysik, D-69029 Heidelberg (Germany)
2. Physics Department, The Ohio State University, Columbus, Ohio 43210 (United States)

We formulate QCD in {ital d}+1 dimensions using Dirac`s front form with periodic boundary conditions, that is, within discretized light-cone quantization. The formalism is worked out in detail for SU(2) pure glue theory in 2+1 dimensions which is approximated by restriction to the lowest {ital transverse} momentum gluons. The dimensionally reduced theory turns out to be an SU(2) gauge theory coupled to adjoint scalar matter in 1+1 dimensions. The scalar field is the remnant of the transverse gluon. This field has modes of both nonzero and zero {ital longitudinal} momentum. We categorize the types of zero modes that occur into three classes, dynamical, topological, and constrained, each well known in separate contexts. The equation for the constrained mode is explicitly worked out. The Gauss law is rather simply resolved to extract physical, namely, color singlet states. The topological gauge mode is treated according to two alternative scenarios related to the elimination of the cutoff. In one, a spectrum is found consistent with pure SU(2) gluons in 1+1 dimensions. In the other, the gauge mode excitations are estimated and their role in the spectrum with genuine Fock excitations is explored. A color singlet state is given which satisfies Gauss` law. Its invariant mass is estimated and discussed in the physical limit.

• OSTI ID: 69565
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 2 Vol. 52; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUNDARY CONDITIONS
EXCITATION
GLUONS
LIGHT CONE
LONGITUDINAL MOMENTUM
QUANTIZATION
QUANTUM CHROMODYNAMICS
SCALAR FIELDS
SU-2 GROUPS
THREE-DIMENSIONAL CALCULATIONS
TRANSVERSE MOMENTUM
TWO-DIMENSIONAL CALCULATIONS