Related papers: Integration on the space of Connections Modulo Gau…
A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools are based on the well-known de Rham-Kodaira decomposing theorem on harmonic…
These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…
The authors establish a relation of the theory of varieties with degenerate Gauss maps in projective spaces with the theory of congruences and pseudocongruences of subspaces and show how these two theories can be applied to the construction…
In this paper we introduce and study some mathematical structures on top of transitive Lie algebroids in order to formulate gauge theories in terms of generalized connections and their curvature: metrics, Hodge star operator and integration…
Recent progress in the construction of both electric, coloured and magnetic charges in gauge theories will be presented. The topological properties of the charged sectors will be highlighted as well as the applications of this work to…
The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…
Phase-space path-integrals are used in order to illustrate various aspects of a recently proposed interpretation of quantum mechanics as a gauge theory of metaplectic spinor fields.
We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182.
In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…
We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field…
We survey several mathematical developments in the holonomy approach to gauge theory. A cornerstone of this approach is the introduction of group structures on spaces of based loops on a smooth manifold, relying on certain homotopy…
We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical…
A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out…
Many moduli spaces are constructed as quotients of group actions; this paper surveys the classical theory, as well as recent progress and applications. We review geometric invariant theory for reductive groups and how it is used to…
A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…
We discuss a recent approach to quantum field theoretical path integration on noncommutative geometries which imply UV/IR regularising finite minimal uncertainties in positions and/or momenta. One class of such noncommutative geometries…
In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…
This note addresses the question whether in a gauge theory coupled to gravity internal and spacetime transformation can be mixed. It is shown that if the VEV of the gauge field is flat, the symmetry group is always a product of internal and…
The variant of electrogravitational unification has been studied on base of principle of relativity of charges and masses.
In this article we examine some points in the moduli space of M-Theory at which there arise enhanced gauge symmetries. In particular, we examine the ``trivial" points of enhanced gauge symmetry in the moduli space of M-Theory on $S^{ 1 }…