Related papers: Braid group statistics in two-dimensional quantum …
Quantum Lorentz groups H admitting quantum Minkowski space V are selected. Natural structure of a quantum space G = V x H is introduced, defining a quantum group structure on G only for triangular H (q=1). We show that it defines a braided…
A presentation of the centralizer of the three-fold tensor product of the spin $s$ representation of the quantum group $U_q(\mathfrak{sl}_2)$ is provided. It is expressed as a quotient of the Askey-Wilson braid algebra. This newly defined…
A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching…
Associated to each subset $J$ of the nodes $I$ of a Dynkin diagram is a triangular decomposition of the corresponding Lie algebra $\mathfrak{g}$ into three subalgebras $\widetilde{\mathfrak{g}_{J}}$ (generated by $e_{j}$, $f_{j}$ for $j\in…
In quantum mechanics, observables correspond to Hermitian operators, and the spectra are restricted to be real. However, the dynamics of the underlying fields may allow complex eigenvalues and therefore create the possibility of braiding…
Modified braid equations satisfied by generalized ${\hat R}$ matrices (for a {\em given} set of group relations obeyed by the elements of ${\sf T}$ matrices ) are constructed for q-deformed quantum groups $GL_q (N), SO_q (N)$ and $Sp_q (N)$…
We introduce color Heisenberg-Lie (super)algebras graded by the abelian groups $Z_3^2$, $Z_2^p\times Z_3^2$ for $p=1,2,3$, and investigate the properties of their associated multi-particle quantum paraoscillators. In the Rittenberg-Wyler's…
We introduce a representation theory of q-Lie algebras defined earlier in \cite{DG1}, \cite{DG2}, formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in…
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our…
We construct local, boost covariant boundary QFT nets of von Neumann algebras on the interior of the Lorentz hyperboloid LH = {x^2 - t^2 > R^2, x>0}, in the two-dimensional Minkowski spacetime. Our first construction is canonical, starting…
Starting from a chiral conformal Haag-Kastler net on 2 dimensional Minkowski space we construct associated charged pointlike localized fields which intertwine between arbitrary superselection sectors with finite statistics of the theory.…
Braid theory is used to calcualte the topological entropy of data from the belousov-Zhabotinskii reaction, the results agree well with one-dimensional theory to the order of approximation considered.
We determine the image of the braid groups inside the Temperley-Lieb algebras, defined over finite field, in the semisimple case, and for suitably large (but controlable) order of the defining (quantum) parameter. We also prove that, under…
Extending the methods from our previous work on quantum knots and quantum graphs, we describe a general procedure for quantizing a large class of mathematical structures which includes, for example, knots, graphs, groups, algebraic…
In this study, we construct a 1+1-dimensional, relativistic, free, complex scalar Quantum Field Theory on the noncommutative spacetime known as lightlike $\kappa$-Minkowski. The associated $\kappa$-Poincar\'e quantum group of isometries is…
Statistical and probabilistic characteristics of locally free group with growing number of generators are defined and their application to statistics of braid groups is given.
Using the ordered analogue of Farley-Sabalka's discrete gradient field on the configuration space of a graph, we unravel a levelwise behavior of the generators of the pure braid group on a tree. This allows us to generalize Farber's…
In this review, we summarize the main ideas of perturbative algebraic quantum field theory, which is a rigorous framework combining some of the Haag-Kastler axioms with perturbative methods involving formal power series. It allows for the…
A rank-2 toric code (R2TC) Hamiltonian in two dimensions can be constructed as a Higgsed descendant of rank-2 U(1) lattice gauge theory. As noted by the authors recently, [Y.-T. Oh, J. Kim, E.-G. Moon, and J. H. Han, Phys. Rev. B {\bf 105},…
We propose an approach to formulating string theory in a curved spacetime, which is based on the connection between the states of the WZW model for the isometry group of a background spacetime metric and the representations of the…