575 research outputs found
1+1 Dimensional Yang-Mills Theories in Light-Cone Gauge
In 1+1 dimensions two different formulations exist of SU(N) Yang Mills
theories in light-cone gauge; only one of them gives results which comply with
the ones obtained in Feynman gauge. Moreover the theory, when considered in
1+(D-1) dimensions, looks discontinuous in the limit D=2. All those features
are proven in Wilson loop calculations as well as in the study of the
bound state integral equation in the large N limit.Comment: Invited report at the Workshop "Low Dimensional Field Theory",
Telluride (CO), Aug. 5-17 1996; 16 pages, latex, no figures To appear in
International Journal of Modern Physics A minor misprints correcte
Gauge Invariance and Anomalous Dimensions of a Light-Cone Wilson Loop in Light-Like Axial Gauge
Complete two-loop calculation of a dimensionally regularized Wilson loop with
light-like segments is performed in the light-like axial gauge with the
Mandelstam-Leibbrandt prescription for the gluon propagator. We find an
expression which {\it exactly} coincides with the one previously obtained for
the same Wilson loop in covariant Feynman gauge. The renormalization of Wilson
loop is performed in the \MS-scheme using a general procedure tailored to the
light-like axial gauge. We find that the renormalized Wilson loop obeys a
renormalization group equation with the same anomalous dimensions as in
covariant gauges. Physical implications of our result for investigation of
infrared asymptotics of perturbative QCD are pointed out.Comment: 24 pages and 4 figures (included), LaTeX style, UFPD-93/TH/23,
UPRF-93-366, UTF-93-29
Two-dimensional Yang-Mills theory in the leading 1/N expansion revisited
We obtain a formal solution of an integral equation for bound
states, depending on a parameter \eta which interpolates between 't Hooft's
(\eta=0) and Wu's (\eta=1) equations. We also get an explicit approximate
expression for its spectrum for a particular value of the ratio of the coupling
constant to the quark mass. The spectrum turns out to be in qualitative
agreement with 't Hooft's as long as \eta \neq 1. In the limit \eta=1 (Wu's
case) the entire spectrum collapses to zero, in particular no rising Regge
trajectories are found.Comment: CERN-TH/96-364, 13 pages, revTeX, no figure
The Mandelstam-Leibbrandt Prescription in Light-Cone Quantized Gauge Theories
Quantization of gauge theories on characteristic surfaces and in the
light-cone gauge is discussed. Implementation of the Mandelstam-Leibbrandt
prescription for the spurious singularity is shown to require two distinct null
planes, with independent degrees of freedom initialized on each. The relation
of this theory to the usual light-cone formulation of gauge field theory, using
a single null plane, is described. A connection is established between this
formalism and a recently given operator solution to the Schwinger model in the
light-cone gauge.Comment: Revtex, 14 pages. One postscript figure (requires psfig). A brief
discussion of necessary restrictions on the light-cone current operators has
been added, and two references. Final version to appear in Z. Phys.
Time exponentiation of a Wilson loop for Yang-Mills theories in 2+\epsilon dimensions
A rectangular Wilson loop centered at the origin, with sides parallel to
space and time directions and length and respectively, is
perturbatively evaluated in Feynman gauge for Yang--Mills
theory in dimensions. When , there is a dependence on the
dimensionless ratio , besides the area. In the limit ,
keeping , the leading expression of the loop involves only the Casimir
constant of the fundamental representation and is thereby in agreement
with the expected Abelian-like time exponentiation (ALTE). At the result
depends also on , the Casimir constant of the adjoint representation and a
pure area law behavior is recovered, but no agreement with ALTE in the limit
. Consequences of these results concerning two and
higher-dimensional gauge theories are pointed out.Comment: RevTex, 28 pages, two figure files include
interaction in light-cone gauge formulations of Yang-Mills theory in 1+1 dimensions
A rectangular Wilson loop with sides parallel to space and time directions is
perturbatively evaluated in two light-cone gauge formulations of Yang-Mills
theory in 1+1 dimensions, with ``instantaneous'' and ``causal'' interactions
between static quarks. In the instantaneous formulation we get Abelian-like
exponentiation of the area in terms of . In the ``causal'' formulation the
loop depends not only on the area, but also on the dimensionless ratio , and being the lengths of the rectangular sides. Besides
it also exhibits dependence on . In the limit the area law
is recovered, but dependence on survives. Consequences of these results
are pointed out.Comment: 30 pages, latex, one figure included as a ps file, an Erratum
include
Renormalization of gauge invariant composite operators in light-cone gauge
We generalize to composite operators concepts and techniques which have been
successful in proving renormalization of the effective Action in light-cone
gauge. Gauge invariant operators can be grouped into classes, closed under
renormalization, which is matrix-wise. In spite of the presence of non-local
counterterms, an ``effective" dimensional hierarchy still guarantees that any
class is endowed with a finite number of elements. The main result we find is
that gauge invariant operators under renormalization mix only among themselves,
thanks to the very simple structure of Lee-Ward identities in this gauge,
contrary to their behaviour in covariant gauges.Comment: 35100 Padova, Italy DFPD 93/TH/53, July 1993
documentstyle[preprint,aps]{revtex
Propagators on the two-dimensional light-cone
Light-cone quantization procedure recently presented is applied to the
two-dimensional light-cone theories. By introducing the two distinct null
planes it is shown that the modification term in the two-dimensional massless
light-cone propagators suggested about twenty years ago vanishs.Comment: LATEX, 9page
Light-Cone Quantization of Gauge Fields
Light-cone quantization of gauge field theory is considered. With a careful
treatment of the relevant degrees of freedom and where they must be
initialized, the results obtained in equal-time quantization are recovered, in
particular the Mandelstam-Leibbrandt form of the gauge field propagator. Some
aspects of the ``discretized'' light-cone quantization of gauge fields are
discussed.Comment: SMUHEP/93-20, 17 pages (one figure available separately from the
authors). Plain TeX, all macros include
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