We extend ideas developed for the loop representation of quantum gravity to diieomorphism-invariant gauge theories coupled to fermions. Let P ! be a principal G-bundle over space and let F be a vector bundle associated to P whose ber is a sum of continuous unitary irreducible representations of the compact connected gauge group G, each representation appearing together with its dual. We conside...

On the total space of a G−complex vector bundle E is defined the gauge transformations. A gauge complex invariant Lagrangian determines a special complex nonlinear connection for which the associated Chern-Lagrange and Bott complex connections are gauge invariant. The complex field equations are determined with respect to these associated gauge complex connections. By complex Legendre transform...

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

We investigate symmetry properties of vector-valued diffusion and Schrödinger equations. For a separable Hilbert space H we characterize the subspaces of L(R , H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge sym...

Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put toward this goal. A set of specific tools which are used in this effort are gauge/gravity dualities. This thesis consists of a specific implementation of ga...

A ten-dimensional supersymmetric gauge theory is written in terms of N = 1, D = 4 superfields. The theory is dimensionally reduced over six-dimensional coset spaces. We find that the resulting four-dimensional theory is either a softly broken N = 1 supersymmetric gauge theory or a non-supersymmetric gauge theory depending on whether the coset spaces used in the reduction are non-symmetric or sy...

Magnetically charged vortex defects are shown to arise in canonically quantised modified axial gauge QCD3+1 on a torus. This gauge – being an Abelian projection – keeps only the eigenphases as dynamical variables of the Wilson line in x3-direction. A mismatch between the identification of large gauge transformations before and after gauge fixing is indicated. Talk presented at the “Workshop on ...

Various aspects of super-space topology and N=l supersymmetry in 2+1 dimensions are explored. Non-Minimal super Yang-Mills theory is used to construct a gauge theory of the N=l super-Poincare’ algebra. A topological super Yang-Mills theory is given and used to compute elements of the cohomology classes of super-monopole moduli space. Submitted to Nuclear Physics B t This work is supported by th...

Quenched reduction is revisited from the modern viewpoint of field-orbifolding. Fermions are included and it is shown how the old problem of preserving anomalies and field topology after reduction is solved with the help of the overlap construction.