72 research outputs found
Induced Operators in QCD
Light-cone quantization always involves the solution of differential
constraint equations. The solutions to these equations include integration
constants (fields independent of ). These fields are unphysical but when
they are consistently removed from the dynamics, additional operators (induced
operators), which would not be present if the integration constants were simply
set to zero, are included in the dynamics. These induced operators can be taken
to act in the usual light-cone subspace, for instance, the space used for DLCQ.
Here, I shall give a derivation of two such operators. The operators are
derived starting from the QCD Lagrangian but the derivation involves some
guesses. The operators will provide for the linear growth of the pion mass
squared with the quark bare mass and for the splitting of the pi and the rho at
zero quark mass.Comment: 8 pages. Talk presented at Light-Cone 2004 at the VU Amsterda
The Mass Operator in the Light-Cone Representation
I argue that for the case of fermions with nonzero bare mass there is a term
in the matter density operator in the light-cone representation which has been
omitted from previous calculations. The new term provides agreement with
previous results in the equal-time representation for mass perturbation theory
in the massive Schwinger model. For the DLCQ case the physics of the new term
can be represented by an effective operator which acts in the DLCQ subspace,
but the form of the term might be hard to guess and I do not know how to
determine its coefficient from symmetry considerations.Comment: Revtex, 8 page
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.
The Vacuum in Light-Cone Field Theory
This is an overview of the problem of the vacuum in light-cone field theory,
stressing its close connection to other puzzles regarding light-cone
quantization. I explain the sense in which the light-cone vacuum is
``trivial,'' and describe a way of setting up a quantum field theory on null
planes so that it is equivalent to the usual equal-time formulation. This
construction is quite helpful in resolving the puzzling aspects of the
light-cone formalism. It furthermore allows the extraction of effective
Hamiltonians that incorporate vacuum physics, but that act in a Hilbert space
in which the vacuum state is simple. The discussion is fairly informal, and
focuses mainly on the conceptual issues. [Talk presented at {\sc Orbis
Scientiae 1996}, Miami Beach, FL, January 25--28, 1996. To appear in the
proceedings.]Comment: 20 pages, RevTeX, 4 Postscript figures. Minor typos correcte
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
Reply to "Comment on 'Light-Front Schwinger Model at Finite Temperature'"
In hep-th/0310278, Blankleider and Kvinikhidze propose an alternate thermal
propagator for the fermions in the light-front Schwinger model. We show that
such a propagator does not describe correctly the thermal behavior of fermions
in this theory and, as a consequence, the claims made in their paper are not
correct.Comment: 3pages, version to be published in Phys. Rev.
The Indispensability of Ghost Fields in the Light-Cone Gauge Quantization of Gauge Fields
We continue McCartor and Robertson's recent demonstration of the
indispensability of ghost fields in the light-cone gauge quantization of gauge
fields. It is shown that the ghost fields are indispensable in deriving
well-defined antiderivatives and in regularizing the most singular component of
gauge field propagator. To this end it is sufficient to confine ourselves to
noninteracting abelian fields. Furthermore to circumvent dealing with
constrained systems, we construct the temporal gauge canonical formulation of
the free electromagnetic field in auxiliary coordinates
where and plays the role of time. In so doing we
can quantize the fields canonically without any constraints, unambiguously
introduce "static ghost fields" as residual gauge degrees of freedom and
construct the light-cone gauge solution in the light-cone representation by
simply taking the light-cone limit (). As a by product we
find that, with a suitable choice of vacuum the Mandelstam-Leibbrandt form of
the propagator can be derived in the case (the temporal gauge
formulation in the equal-time representation).Comment: 21 pages, uses ptptex.st
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