Peculiarities of the Canonical Analysis of the First Order Form of the Einstein-Hilbert Action in Two Dimensions in Terms of the Metric Tensor or the Metric Density

The peculiarities of doing a canonical analysis of the first order formulation of the Einstein-Hilbert action in terms of either the metric tensor $g^{\alpha \beta}$ or the metric density $h^{\alpha \beta}= \sqrt{-g}g^{\alpha \beta}$ along with the affine connection are discussed. It is shown that the difference between using $g^{\alpha \beta}$ as opposed to $h^{\alpha \beta}$ appears only in two spacetime dimensions. Despite there being a different number of constraints in these two approaches, both formulations result in there being a local Poisson brackets algebra of constraints with field independent structure constants, closed off shell generators of gauge transformations and off shell invariance of the action. The formulation in terms of the metric tensor is analyzed in detail and compared with earlier results obtained using the metric density. The gauge transformations, obtained from the full set of first class constraints, are different from a diffeomorphism transformation in both cases.Comment: 13 page

On the role of vector mesons in topological soliton stability

Isospin one vector mesons (in particular the $\rho$) are usually described as massive Yang-Mills particles in the chiral Lagrangian. We investigate some aspects of an alternative approach in the soliton sector. It is found that the soliton is stable in very much the same way as with the $\omega$-meson and that spontaneous parity violating classical solutions do not exist. The formulation in terms of antisymmetric tensors is shown to be canonically related to a vector field description provided the Skyrme term is added to the latter.Comment: 10 pages, plain TEX, 1 figure (not included) IPN Orsay report IPNO/TH 92-8

An algebraic interpretation of the Wheeler-DeWitt equation

We make a direct connection between the construction of three dimensional topological state sums from tensor categories and three dimensional quantum gravity by noting that the discrete version of the Wheeler-DeWitt equation is exactly the pentagon for the associator of the tensor category, the Biedenharn-Elliott identity. A crucial role is played by an asymptotic formula relating 6j-symbols to rotation matrices given by Edmonds.Comment: 10 pages, amstex, uses epsf.tex. New version has improved presentatio

The Role of Zero-Modes in the Canonical Quantization of Heavy-Fermion QED in Light-Cone Coordinates

Four-dimensional heavy-fermion QED is studied in light-cone coordinates with (anti-)periodic field boundary conditions. We carry out a consistent light-cone canonical quantization of this model using the Dirac algorithm for a system with first- and second-class constraints. To examine the role of the zero modes, we consider the quantization procedure in {the }zero-mode {and the non-zero-mode} sectors separately. In both sectors we obtain the physical variables and their canonical commutation relations. The physical Hamiltonian is constructed via a step-by-step exclusion of the unphysical degrees of freedom. An example using this Hamiltonian in which the zero modes play a role is the verification of the correct Coulomb potential between two heavy fermions.Comment: 22 pages, CWRUTH-93-5 (Latex

Light Front Quantization

An introductory overview on Light-Front quantization, with some emphasis on recent achievements, is given. Light-Front quantization is the most promising and physical tool to study deep inelastic scattering on the basis of quark gluon degrees of freedom. The simplified vacuum structure (nontrivial vacuum effects can only appear in zero-mode degrees of freedom) and the physical basis allows for a description of hadrons that stays close to intuition. Recent progress has ben made in understanding the connection between effective LF Hamiltonians and nontrivial vacuum condesates. Discrete Light-Cone Quantization, the transverse lattice and Light-Front Tamm-Dancoff (in combination with renormalization group techniques) are the main tools for exploring LF-Hamiltonians nonperturbatively.Comment: LATEX, 87 pages, postscript files for the figures or a postscript file for the complete article (900 kB) available from the autho