相关论文: Quantized trace rings

Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…

We generalize Bonahon-Wong's $\mathrm{SL}_2(\mathbb{C})$-quantum trace map to the setting of $\mathrm{SL}_3(\mathbb{C})$. More precisely, given a non-zero complex parameter $q=e^{2 \pi i \hbar}$, we associate to each isotopy class of framed…

In the context of constrained quantum mechanics, reference systems are used to construct relational observables that are invariant under the action of the symmetry group. Upon measurement of a relational observable, the reference system…

It is well--known that if one is given a principal $G$--bundle with a principal connection, then for every unitary finite--dimensional linear representation of $G$ one can induce a linear connection and a Hermitian structure on the…

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…

Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. We show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant…

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…

The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…

This article investigates the traces of certain modules over rings of invariants associated with finite groups. More precisely, we provide a formula for computing the traces of arbitrary semi-invariants, thereby contributing to the…

In the recent years a lot of attention is focused on unconventional string compactifications. A variety of different but related frameworks was developed in order to address issues such as duality invariance, non-geometry and…

We construct an explicit categorification of the action of tangles on tensor powers of the fundamental representation of quantum sl(2).

In math.GR/0510298, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the equational class of (pointed) F-quasigroups and…

A group element is called a generalized torsion if a finite product of its conjugates is equal to the identity. We prove that in a nilpotent or FC-group, the generalized torsion elements are all torsion elements. Moreover, we compute the…

In this paper, we establish a determinantal formula for 2 x 2 matrix commutators [X,Y] = XY - YX over a commutative ring, using (among other invariants) the quantum traces of X and Y. Special forms of this determinantal formula include a…

We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the…

The orthogonal group acts on the space of several $n\times n$ matrices by simultaneous conjugation. For an infinite field of characteristic different from two, relations between generators for the algebra of invariants are described. As an…

We study the problem when every matrix over a division ring is representable as either the product of traceless matrices or the product of semi-traceless matrices, and also give some applications of such decompositions. Specifically, we…

We investigate the dynamics of quantum entanglement and more general quantum correlations quantified respectively via negativity and local quantum uncertainty for two qubit systems undergoing Markovian collective dephasing. Focusing on a…

Quantum Rings have been simulated so far in many ways, but in this work a new aproximation is deemed. We use particles without angular momentum and several spectra, for different geometric settings, are gotten. These spectra depends on K,…

For harnessing the full potential of quantum phenomena, light-matter interfaces and complexly connected quantum networks are required, relying on the joint quantum operation of different physical platforms. In this work, we analyze the…