The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing at a space-time level the whole gauge group SO(1, 3)×U(1)×SU(2)×SU(3) associated to fundamental interactions; equivalently, by assuming that internal gauge tr...

We know that there is an isomorphism between the moduli space of gauge equivalence classes of flat G-connections on a compact surface and the moduli space of representations from the fundamental group of the surface to G acted on by the adjoint action (cf: Goldman[G]). It is known that if G is compact, semi-simple and simply connected, the moduli space of gauge equivalence classes of flat G-con...

It is shown how a metric structure can be induced in a simple way starting with a gauge structure and a preferred volume, by spontaneous symmetry breaking. A polynomial action, including coupling to matter, is constructed for the symmetric phase. It is argued that assuming a preferred volume, in the context of a metric theory, induces only a limited modification of the theory. §1 Attempts to Us...

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2, 2) gauge transformations acting on the spinor index of the wave functions. This local U(2, 2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory. 1 Connection between Local Gauge ...

A method of path integral construction without gauge fixing in the holomorphic representation is proposed for finite-dimensional gauge models. This path integral determines a manifestly gauge-invariant kernel of the evolution operator. 1. It is well known that a gauge symmetry leads to constraints on dynamical variables in the theory [1]. Therefore, the evolution of unphysical degrees of freedo...

We first apply Connes’ noncommutative geometry to a finite point space. The explicit form of the action functional of U(1) gauge field on this n-point space is obtained. We then consider the case when the npoint space is replaced by {space-time} × {n-point space}. This action is shown to relate the Hamiltonian of the continuous-spin formulation of the Potts model. We argue that U(1) gauge theor...

We first extend the Peierls algebra of gauge invariant functions from the space S of classical solutions to the space H of histories used in path integration and some studies of decoherence. We then show that it may be generalized in a number of ways to act on gauge dependent functions on H. These generalizations (referred to as class I) depend on the choice of an “invariance breaking term,” wh...

As a tool to carry out the quantization of gauge theory on a noncommutative space, we present a Dirac operator that behaves as a line element of the canonical noncommutative space. Utilizing this operator, we construct the Dixmier trace, which is the regularized trace for infinite-dimensional matrices. We propose the possibility of solving the cosmological constant problem by applying our gauge...

In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be extended to face these kinematical non-linearities squarely. We first present a pedagogical account of this problem and then suggest an avenue for its resolution.