Related papers: Handle Operators in R.C.F.T
In this paper, we discuss the inverse problem of determining a semisimple group algebra from the knowledge of rings of the type sum_{t=1}^s M_{n_t}(Ft), where j is an arbitrary integer and F_t is finite field for each t, and show that it is…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
We describe various handle moves in contact surgery diagrams, notably contact analogues of the Kirby moves. As an application of these handle moves, we discuss the respective classifications of long and loose Legendrian knots.
Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter operator on a group. We provide some general constructions of…
We consider toy models of holography arising from 3d Chern-Simons theory. In this context a duality to an ensemble average over 2d CFTs has been recently proposed. We put forward an alternative approach in which, rather than summing over…
The paper is devoted to the index theory of orbital and transverse elliptic operators on manifolds with a proper Lie group action. It corrects errors of my previous paper (published in JNCG in 2016) on transverse operators and contains new…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
The cut and join operations play important roles in tensor models in general. We introduce a generalization of the cut operation associated with the higher order variations and demonstrate how they generate operators in the Aristotelian…
Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli…
We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…
We propose a (4+1) dimensional Chern-Simons field theoretical description of the fractional quantum Hall effect. It suggests that composite fermions reside on a momentum manifold with a nonzero Chern number. Based on derivations from…
We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
We formulate the Chern-Simons action for any compact Lie group using Deligne cohomology. This action is defined as a certain function on the space of smooth maps from the underlying 3-manifold to the classifying space for principal bundles.…
Given parameters $x \notin \mathbb{R}^- \cup \{1\}$ and $\nu$, $\mathrm{Re}(\nu) < 0$, and the space $\mathscr{H}_0$ of entire functions in $\mathbb{C}$ vanishing at $0$, we consider the family of operators $\mathfrak{L} = c_0 \cdot \delta…
Reshetikhin-Turaev (a.k.a. Chern-Simons) TQFT is a functor that associates vector spaces to two-dimensional genus g surfaces and linear operators to automorphisms of surfaces. The purpose of this paper is to demonstrate that there exists a…
Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and properties that are implicit in universal algebra and…
A direct relation between two types of topological field theories, Chern-Simons theory and BF theory, is presented by using ``Generalized Differential Calculus'', which extends an ordinary p-form to an ordered pair of p and (p+1)-form. We…
Geometrical meaning of superstring pictures is discussed in details. An off-shell generalization of the picture changing operation and its inverse are constructed. It is demonstrated that the generalised operations are inverse to each other…
Chern-Simons field theory based on a compact non-abelian gauge group is studied as a theory of knots and links in three dimensions. A method to obtain the invariants for links made from braids of upto four strands is developed. This…