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

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 $x_-$). 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 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 $x^{\mu}=(x^-,x^+,x^1,x^2)$ where $x^-=x^0 cos{\theta}-x^3 sin{\theta}, x^+=x^0 sin{\theta}+x^3 cos{\theta}$ and $x^-$ 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 (${\theta}\to \pi/4$). 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 ${\theta}=0$ case (the temporal gauge formulation in the equal-time representation).Comment: 21 pages, uses ptptex.st