Related papers: Bundle Gerbes Applied to Quantum Field Theory
Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…
Given a representation N of a reductive group G, Braverman-Finkelberg-Nakajima have defined a remarkable Poisson variety called the Coulomb branch. Their construction of this space was motivated by considerations from 3d gauge theories and…
Let $(P, Y)$ be a bundle gerbe over a fibre bundle $Y \to M$. We show that if $M$ is simply-connected and the fibres of $Y \to M$ are connected and finite-dimensional then the Dixmier-Douady class of $(P, Y)$ is torsion. This corrects and…
An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal $G$-bundle with connection and a class in $H^4(BG, \ZZ)$ for a compact semi-simple Lie group $G$. The Chern-Simons bundle…
An alternative approach to lattice gauge theory has been under development for the past decade. It is based on discretizing the operator Heisenberg equations of motion in such a way as to preserve the canonical commutation relations at each…
We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)], which describes (1+1) quantum electrodynamics of an Abelian $U(1)$ gauge field coupled to a symmetry-protected topological matter sector, by…
The present paper is the first in a series of papers, in which we shall construct modular functors and Topological Quantum Field Theories from the conformal field theory developed in [TUY]. The basic idea is that the covariant constant…
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with…
Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
We discuss the possibility to construct an effective quantum field theory for an axial vector coupled to a Dirac spinor field. A massive axial vector describes antisymmetric torsion. The consistency conditions include unitarity and…
The observation that spacetime and quantum fields on it have to be dynamically produced in any theory of quantum gravity implies that quantum gravity should be defined on the configuration space of fields rather than spacetime. Such a…
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…
A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on…
We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible…
We develop the field space geometry of scalar-fermion effective field theories as a vector bundle supermanifold. We further establish a Fermi normal coordinate system on the bundle that clarifies the geometric content in scattering…
We establish the spin-statistics theorem for topological quantum field theories (TQFTs) in the framework of Atiyah. We incorporate spin via spin structures on bordisms, and represent statistics using super vector spaces. Unitarity is…
We construct canonical quantum fields which propagate on a star graph modeling a quantum wire. The construction uses a deformation of the algebra of canonical commutation relations, encoding the interaction in the vertex of the graph. We…