Related papers: Bundle Gerbes Applied to Quantum Field Theory
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principle fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the…
We provide an extension of the Gromov--Zimmer Embedding Theorem for Cartan geometries of [3] to tractor bundles carrying any invariant connection, including tractor connections and prolongation connections of first BGG operators for…
We consider Real bundle gerbes on manifolds equipped with an involution and prove that they are classified by their Real Dixmier-Douady class in Grothendieck's equivariant sheaf cohomology. We show that the Grothendieck group of Real bundle…
The Atiyah-Singer index theorem is investigated on various compact manifolds which admit finite matrix approximations (``fuzzy spaces'') with a view to applications in a modified Kaluza-Klein type approach in which the internal space…
A equivalence relation, preserving the Chern-Weil form, is defined between connections on a complex vector bundle. Bundles equipped with such an equivalence class are called Structured Bundles, and their isomorphism classes form an abelian…
A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore…
We give a very simple derivation of the Atiyah-Patodi-Singer (APS) index theorem and its small generalization by using the path integral of massless Dirac fermions. It is based on the Fujikawa's argument for the relation between the axial…
On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the…
We construct equivariant vector bundles over quantum projective spaces making use of parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of projective space as a…
Long strings emerge in many Quantum Field Theories, for example as vortices in Abelian Higgs theories, or flux tubes in Yang-Mills theories. The actions of such objects can be expanded in the number of derivatives, around a long straight…
The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…
In this paper, we start from an extension of the notion of holonomy on diffeological bundles, reformulate the notion of regular Lie group or Fr\"olicher Lie groups, state an Ambrose-Singer theorem that enlarges the one stated in \cite{Ma2},…
The non-associativity of translations in a quantum system with magnetic field background has received renewed interest in association with topologically trivial gerbes over $\mathbb{R}^n.$ The non-associativity is described by a 3-cocycle…
The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…
Many bundle gerbes constructed in practice are either infinite-dimensional, or finite-dimensional but built using submersions that are far from being fibre bundles. Murray and Stevenson proved that gerbes on simply-connected manifolds,…
F-bundle is a formal/non-archimedean version of variation of nc-Hodge structures which plays a crucial role in the theory of atoms as birational invariants from Gromov-Witten theory. In this paper, we establish the spectral decomposition…
Consistent and covariant Lorentz and diffeomorphism anomalies are investigated in terms of the geometry of the universal bundle for gravity. This bundle is explicitly constructed and its geometrical structure will be studied. By means of…