相关论文: Conserved Quantities and the Algebra of Braid Exci…
We use the conservation law of the stress-energy and spin tensors to study the motion of massive brane-like objects in Riemann-Cartan geometry. The world-sheet equations and boundary conditions are obtained in a manifestly covariant form.…
It is shown that every quantum principal bundle is braided, in the sense that there exists an intrinsic braid operator twisting the functions on the bundle. A detailed algebraic analysis of this operator is performed. In particular, it…
General braided counterparts of classical Clifford algebras are introduced and investigated. Braided Clifford algebras are defined as Chevalley-Kahler deformations of the corresponding braided exterior algebras. Analogs of the spinor…
We show that the effective dynamics of matter fields coupled to 3d quantum gravity is described after integration over the gravitational degrees of freedom by a braided non-commutative quantum field theory symmetric under a…
We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are…
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…
Quantum algebras U_q(su_n) used as the algebras of flavour symmetry (usually described by SU(n)) to study static properties of hadrons lead to intriguing results. In this contribution we focus on the peculiar properties manifested by…
We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for $n$-point functions. Perturbation theory leads us to…
We propose a new non-commutative generalization of the representation variety and the character variety of a knot group. Our strategy is to reformulate the construction of the algebra of functions on the space of representations in terms of…
We introduce Natural Qubit Algebra (NQA), a compact real operator calculus for qubit systems based on a $2\times2$ block alphabet $\{I,X,Z,W\}\subset\mathrm{Mat}(2,\mathbb{R})$ and tensor-word representations. The resulting multiplication…
A common choice for the evolution of the knotted graphs in loop quantum gravity is to use the Pachner moves, adapted to graphs from their dual triangulations. Here, we show that the natural way to consistently use these moves is on framed…
Quantum matrices $A(R)$ are known for every $R$ matrix obeying the Quantum Yang-Baxter Equations. It is also known that these act on `vectors' given by the corresponding Zamalodchikov algebra. We develop this interpretation in detail,…
We study the behavior of representation varieties of quivers with relations under the operation of node splitting. We show how splitting a node gives a correspondence between certain closed subvarieties of representation varieties for…
An extension of the Artin Braid Group with new operators that generate double and triple intersections is considered. The extended Alexander theorem, relating intersecting closed braids and intersecting knots is proved for double and triple…
It is shown that expected values of free scalar and vector quantum fields on graphs satisfy the same conservation laws as the classic fields. It is demonstrated that a modified version of conservation laws is satisfied for Villain action.…
We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed…
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…
We give a pedagogical introduction to integration techniques appropriate for non-commutative spaces while presenting some new results as well. A rather detailed discussion outlines the motivation for adopting the Hopf algebra language. We…
We review some perturbative results obtained in quantum gravity in an accelerating cosmological background. We then describe a class of non-local, purely gravitational models which have the correct structure to reproduce the leading…
We construct the join of noncommutative Galois objects (quantum torsors) over a Hopf algebra H. To ensure that the join algebra enjoys the natural (diagonal) coaction of H, we braid the tensor product of the Galois objects. Then we show…