24 research outputs found
Towards Solving QCD - The Transverse Zero Modes in Light-Cone Quantization
We formulate QCD in (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 {\it transverse}
momentum gluons. The dimensionally-reduced theory turns out to be 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 non-zero
and zero {\it 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 In the 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.Comment: LaTex document, 26 pages, one figure (obtainable by contacting
authors). To appear in Physical. Review
Dynamical Zero Modes and Pure Glue in Light-Cone Field Theory
We consider light-cone quantized on a `cylinder' with
periodic boundary conditions on the gluon fields. This is the framework of
discretized light-cone quantization. We review the argument that the light-cone
gauge is not attainable. The zero mode is a dynamical and gauge
invariant field. The attainable gauge has a Gribov ambiguity. We exactly solve
the problem of pure glue theory coupled to some zero mode external sources. We
verify the identity of the front and the more familiar instant form approaches.
We obtain a discrete spectrum of vacuum states and their wavefunctions.Comment: 13 pages LaTex report#: OHSTPY-HEP-TH-94-001, MPIH-V9-94 Revised
version 2-- minor changes to equations and discussion. Submitted to Physical
Review