Related papers: Spin Topological Quantum Field Theories
Motivated by suggestions of Paolo Cotta-Ramusino's work at the physical level of rigor relating BF theory to the Donaldson polynomials, we provide a construction applicable to the Turaev/Viro and Crane/Yetter invariants of *a priori* finer…
We study the transition amplitudes in state-sum models of quantum gravity in D=2,3,4 spacetime dimensions by using the field theory over a Lie group formulation. By promoting the group theory Fourier modes into creation and annihilation…
In this expository paper we introduce extended topological quantum field theories and the cobordism hypothesis.
We review the q-deformed spin network approact to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. These methods produce a concise proof…
The goal of this work is to describe a categorical formalism for (Extended) Topological Quantum Field Theories (TQFTs) and present them as functors from a suitable category of cobordisms with corners to a linear category, generalizing 2d…
We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…
We prove a theorem in 3-dimensional topological field theory: a Reshetikhin-Turaev theory admits a nonzero boundary theory iff it is a Turaev-Viro theory. The proof immediately implies a characterization of fusion categories in terms of…
In this paper, we introduce the concept of 3-alterfolds with embedded separating surfaces. When the separating surface is decorated by a spherical fusion category, we obtain quantum invariants of 3-alterfold, which is consistent with many…
We classify closed, topological spin$^+$ 4-manifolds with fundamental group $\pi$ of cohomological dimension $\leq 3$ (up to s-cobordism), after stabilization by connected sum with at most $b_3(\pi)$ copies of $S^2\times S^2$. In general we…
We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate an invariant to each ciliated surface, which is a Laurent…
A modular tensor category $\mathcal{C}$ gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal{C}$-coloured ribbon graphs. We extend this construction to…
One-dimensional quantum rings with Rashba and Dresselhaus spin-orbit couplings are studied analytically and are in perfect agreement with the numerical results. The topological charge of the spin field defined by the winding number along…
We give a combinatorial model for r-spin surfaces with parametrised boundary based on Novak (2015). The r-spin structure is encoded in terms of $\mathbb{Z}_r$-valued indices assigned to the edges of a polygonal decomposition. This…
A new topological field theory is constructed, which is characterized by cubic interactions similar to those of non-abelian Chern-Simons field theories, but still retains the simplicity of the abelian case. The perturbative expansion of…
We construct a quantisation of the Teichmueller spaces of super Riemann surfaces using coordinates associated to ideal triangulations of super Riemann surfaces. A new feature is the non-trivial dependence on the choice of a spin structure…
Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
We use the approach to generate spin foam models by an auxiliary field theory defined on a group manifold (as recently developed in quantum gravity and quantization of BF-theories) in the context of topological quantum field theories with a…
We concretely construct a 2-categorically extended TQFT that extends the Reshetikhin-Turaev TQFT to cobordisms with corners. The source category will be a well chosen 2-category of decorated cobordisms with corners and the target bicategory…
We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or…