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Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
We construct a new type of S-matrix in quantum field theory using the general boundary formulation. In contrast to the usual S-matrix the space of free asymptotic states is located at spatial rather than at temporal infinity. Hence, the new…
S-matrix elements in flat space can be obtained from a large AdS-radius limit of certain CFT correlators. We present a method for constructing CFT operators which create incoming and outgoing scattering states in flat space. This is done by…
A noncommutative-geometric generalization of the classical formalism of frame bundles is developed, incorporating into the theory of quantum principal bundles the concept of the Levi-Civita connection. The construction of a natural…
We compare the quantisation of linear systems of bosons and fermions. We recall the appearance of projectively flat connection and results on parallel transport in the quantisation of bosons. We then discuss pre-quantisation and…
We observe that, within the effective generating function formalism for the implementation of canonical transformations within wave mechanics, non-trivial canonical transformations which leave invariant the form of the Hamilton function of…
We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a…
We consider non-perturbative superpotentials from world-sheet instantons wrapped on holomorphic genus zero curves in heterotic string theory. These superpotential contributions feature prominently in moduli stabilization and large field…
We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of…
Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that 4-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's…
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic…
We introduce group actions on polyfolds and polyfold bundles. We prove quotient theorems for polyfolds, when the group action has finite isotropy. We prove that the sc-Fredholm property is preserved under quotient if the base polyfold is…
Let $X$ be a connected, compact complex manifold and $S\subset X$ a separating real hypersurface, so that $X$ decomposes as a union of compact complex manifolds with boundary $\bar X^\pm$. Let $\mathcal{M}$ be the moduli space of $S$-framed…
We study the quantization of spaces whose K-theory in the classical limit is the ring of dual numbers $\mathbb{Z}[t]/(t^2)$. For a compact Hausdorff space we recall necessary and sufficient conditions for this to hold. For a compact quantum…
By means of simple models in a flat spacetime manifold we examine some of the issues that arise when quantizing interacting quantum fields in multi-metric backgrounds. In particular we investigate the maintenance of a causal structure in…
Unitary Representations corresponding to local shifts in reference frames are a key topic for progress in Quantum Gravity. The fibre bundle construct defined in our previous work in which quantum fields become liftings of; or sections…
The issue of non-perturbative background independent quantization of matrix models is addressed. The analysis is carried out by considering a simple matrix model which is a matrix extension of ordinary mechanics reduced to 0 dimension. It…
Path integral formulation of quantum mechanics defines the wavefunction associated with a particle as a sum of phase-factors, which are periodic functions of classical action. In the present article, this periodicity is shown to impart the…
We study the symmetry resolution of the entanglement entropy of an interval in two-dimensional conformal field theories (CFTs), by relating the bipartition to the geometry of an annulus with conformal boundary conditions. In the presence of…
In this thesis, we explore two approaches to string phenomenology. In the first half of the work, we investigate M-theory compactifications on spaces with co-dimension four, orbifold singularities. We construct M-theory on C^2/Z_N by…