A (1+1)-Dimensional Reduced Model of Mesons

We propose an extension of 't Hooft's large-$N_c$ light-front QCD in two dimensions to include helicity and physical gluon degrees of freedom, modelled on a classical dimensional reduction of four dimensional QCD. A non-perturbative renormalisation of the infinite set of coupled integral equations describing boundstates is performed. These equations are then solved, both analytically in a phase space wavefunction approximation and numerically by discretising momenta, for (hybrid) meson masses and (polarized) parton structure functions.Comment: LaTex 13 pages; 2 figures, uuencoded file (PostScript

On the Transition from Confinement to Screening in QCD_{1+1} Coupled to Adjoint Fermions at Finite N

We consider SU(N) QCD_{1+1} coupled to massless adjoint Majorana fermions, where N is finite but arbitrary. We examine the spectrum for various values of N, paying particular attention to the formation of multi-particle states, which were recently identified by Gross, Hashimoto and Klebanov in the N -> infinity limit of the theory. It is believed that in the limit of vanishing fermion mass, there is a transition from confinement to screening in which string-like states made out of adjoint fermion bits dissociate into stable constituent ``single particles''. In this work, we provide numerical evidence that such a transition into stable constituent particles occurs not only at large N, but for any finite value of N. In addition, we discuss certain issues concerning the ``topological'' properties exhibited by the DLCQ spectrum.Comment: 14 pages, Late

Quantum Chromodynamics and Other Field Theories on the Light Cone

We discuss the light-cone quantization of gauge theories as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The light-cone Fock state expansion of wavefunctions provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of light-cone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavy-quark contributions to structure functions. Discretized light-cone quantization, is outlined and applied to several gauge theories. We also discuss the construction of the light-cone Fock basis, the structure of the light-cone vacuum, and outline the renormalization techniques required for solving gauge theories within the Hamiltonian formalism on the light cone.Comment: 206 pages Latex, figures included, Submitted to Physics Report

Renormalization of an effective Light-Cone QCD-inspired theory for the Pion and other Mesons

The renormalization of the effective QCD-Hamiltonian theory for the quark-antiquark channel is performed in terms of a renormalized or fixed-point Hamiltonian that leads to subtracted dynamical equations. The fixed point-Hamiltonian brings the renormalization conditions as well as the counterterms that render the theory finite. The approach is renormalization group invariant. The parameters of the renormalized effective QCD-Hamiltonian comes from the pion mass and radius, for a given constituent quark mass. The 1s and excited 2s states of $\bar u q$ are calculated as a function of the mass of the quark $q$ being s, c or b, and compared to the experimental values.Comment: 39 pages, 10 figure

Light-Front QCD(1+1) Coupled to Adjoint Scalar Matter

We consider adjoint scalar matter coupled to QCD(1+1) in light-cone quantization on a finite `interval' with periodic boundary conditions. We work with the gauge group SU(2) which is modified to ${\rm{SU(2)/Z_2}}$ by the non-trivial topology. The model is interesting for various nonperturbative approaches because it is the sector of zero transverse momentum gluons of pure glue QCD(2+1), where the scalar field is the remnant of the transverse gluon component. We use the Hamiltonian formalism in the gauge $\partial_- A^+ = 0$. What survives is the dynamical zero mode of $A^+$, which in other theories gives topological structure and degenerate vacua. With a point-splitting regularization designed to preserve symmetry under large gauge transformations, an extra $A^+$ dependent term appears in the current $J^+$. This is reminiscent of an (unwanted) anomaly. In particular, the gauge invariant charge and the similarly regulated $P^+$ no longer commute with the Hamiltonian. We show that nonetheless one can construct physical states of definite momentum which are not {\it invariant} under large gauge transformations but do {\it transform} in a well-defined way. As well, in the physical subspace we recover vanishing {\it expectation values} of the commutators between the gauge invariant charge, momentum and Hamiltonian operators. It is argued that in this theory the vacuum is nonetheless trivial and the spectrum is consistent with the results of others who have treated the large N, SU(N), version of this theory in the continuum limit.Comment: LaTex, 13 pages. Submitted to Physics Letters

Transient effects on electron spin observation

In an earlier publication we addressed the problem of splitting an electron beam in the Stern-Gerlach experiment. In contrast to arguments put forward in the early days of quantum theory, we concluded that there are no issues of principle preventing the observation of electron spin during free flight. In that paper, however, we considered only a sudden switch off of the separating magnetic field. In this work we consider the possible effects of finite switching times at the beginning and the end of the interaction period. We consider a model where the coupling between the electron and the field is time dependent. As a result of the time dependence, the field also acquires an electric component, but this seems to cause no significant change of our conclusions. On the other hand, the smooth change of the interaction enforces the same longitudinal velocity on the electron both at the beginning and end of the interaction period because of conservation laws; this effect was missing in our earlier calculations. As the electrons are supposed to travel as a beam, this feature helps by restoring the beam quality after the interaction

Transverse Lattice QCD in 2+1 Dimensions

Following a suggestion due to Bardeen and Pearson, we formulate an effective light-front Hamiltonian for large-N gauge theory in (2+1)-dimensions. Two space-time dimensions are continuous and the remaining space dimension is discretised on a lattice. Eguchi-Kawai reduction to a (1+1)-dimensional theory takes place. We investigate the string tension and glueball spectrum, comparing with Euclidean Lattice Monte Carlo data.Comment: 4 pages LaTeX with 2 Postscript figures, uses boxedeps.tex and e spcrc2.sty. Poster session contribution to LATTICE96(poster). Minor changes in new versio

Towards Solving QCD in Light-Cone Quantization -- On the Spectrum of the Transverse Zero Modes for SU(2)

The formalism for a non-abelian pure gauge theory in (2+1) dimensions has recently been derived within Discretized Light-Cone Quantization, restricting to the lowest {\it transverse} momentum gluons. It is argued why this model can be a paradigm for full QCD. The physical vacuum becomes non-trivial even in light-cone quantization. The approach is brought here to tractable form by suppressing by hand both the dynamical gauge and the constraint zero mode, and by performing a Tamm-Dancoff type Fock-space truncation. Within that model the Hamiltonian is diagonalized numerically, yielding mass spectra and wavefunctions of the glue-ball states. We find that only color singlets have a stable and discrete bound state spectrum. The connection with confinement is discussed. The structure function of the gluons has a shape like $[{x(1-x)}] ^{1\over 3}$. The existence of the continuum limit is verified by deriving a coupled set of integral equations.Comment: 1 Latex file & 9 Postscript files; tarred, compressed and uuencode

Tube Model for Light-Front QCD

We propose the tube model as a first step in solving the bound state problem in light-front QCD. In this approach we neglect transverse variations of the fields, producing a model with 1+1 dimensional dynamics. We then solve the two, three, and four particle sectors of the model for the case of pure glue SU(3). We study convergence to the continuum limit and various properties of the spectrum.Comment: 29 page