Related papers: Orbifold groupoids
In this paper, we study the $G$-representation and character varieties of non-orientable closed surfaces. By means of a geometric method based on a Topological Quantum Field Theory (TQFT), we compute the virtual classes of these varieties…
We explain a strategy, based on spectral invariants on symmetric product orbifolds, for proving the smooth closing lemma for Hamiltonian diffeomorphisms of a symplectic manifold when the orbifold quantum cohomologies of its symmetric…
We use the 3D SymTFT approach to study the generalized symmetries and partition functions of 2D CFTs in various orbifolded and fermionic phases. These phases can be realized by the sandwich construction in the associated 3D SymTFTs with…
The unitary Clifford algebras are described here for the first time, and arise from the intersection of the orthogonal and common symplectic (Weyl) Clifford algebras of the complexification of the canonical phase space. The convergence of…
We explore algebraic characterizations of 2-knots whose associated knot manifolds fibre over lower-dimensional orbifolds, and consider also some issues related to the groups of higher-dimensional fibred knots.
We construct bosonic and fermionic matrix-vector models which describe orbifolded string worldsheets at a limit in which the dimension of the vector space and the matrix order are taken to infinity. We evaluate tree-level one-loop or…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
In this paper we will analyse some interesting structures that occur in scalar quantum field theory. We will quantize this theory using path integrals. We will analyse the Bogomolny Bound for scalar quantum field theory in two dimensions.…
In canonical quantum gravity certain topological properties of 3-manifolds are of interest. This article gives an account of those properties which have so far received sufficient attention, especially those concerning the diffeomorphism…
In this paper we study the Real Gromov-Witten theory of local 3-folds over Real curves. We show that this gives rise to a 2-dimensional Klein TQFT defined on an extension of the category of unorientable surfaces. We use this structure to…
For p>3 a prime, and g>2 an integer, we use Topological Quantum Field Theory (TQFT) to study a family of p-1 highest weight modules L_p(lambda) for the symplectic group Sp(2g,K) where K is an algebraically closed field of characteristic p.…
We formulate a quantum group analogue of the group of orinetation-preserving Riemannian isometries of a compact Riemannian spin manifold, more generally, of a (possibly $R$-twisted in the sense of a paper of one of the authors, and of…
The q-special functions appear naturally in q-deformed quantum mechanics and both sides profit from this fact. Here we study the relation between the q-deformed harmonic oscillator and the q-Hermite polynomials. We discuss: recursion…
The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been…
For more than half a century, covariant and differential geometric methods have been playing a central role in the development of Quantum Field Theory (QFT). After a brief historic overview of the major scientific achievements using these…
We study the spectrum of permutation orbifolds of 2d CFTs. We find examples where the light spectrum grows faster than Hagedorn, which is different from known cases such as symmetric orbifolds. We also describe how to compute their…
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a…
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…
This PhD Thesis is devoted to the study of Hodge structures on a special type of complex algebraic varieties, the so-called character varieties. For this purpose, we propose to use a powerful algebro-geometric tool coming from theoretical…
The main purpose of this paper is to give a generalization of Dijkgraaf-Witten theory. Consider a morphism from a smash product of spectra E,F to another spectrum G. We construct a TQFT for E-oriented manifolds using a representative of an…