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We consider the path integral of a quantum field theory in Minkowski spacetime with fixed boundary values (for the elementary fields) on asymptotic boundaries. We define and study the corresponding boundary correlation functions obtained by…
Exploiting the path integral approach al la Batalin and Vilkovisky, we show that any anomaly-free Quantum Field Theory (QFT) comes with a family parametrized by certain moduli space M, which tangent space at the point corresponding to the…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…
Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their…
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
In "On the calculation of some differential Galois groups" (Invent. Math. 87 (1987), no. 1), Katz defines the notion of a special flat connection on the complex affine line minus the origin, and he shows that the functor which restricts a…
It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of…
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 propose a new fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
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…
We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory,…
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…
We introduce the concept of a quantum background and a functor QFT. In the case that the QFT moduli space is smooth formal, we construct a flat quantum superconnection on a bundle over QFT which defines algebraic structures relevant to…
We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions…
We study boundary conditions for extended topological quantum field theories (TQFTs) and their relation to topological anomalies. We introduce the notion of TQFTs with moduli level $m$, and describe extended anomalous theories as natural…
Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and…