Related papers: On the q-quantum gravity loop algebra
q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…
The $q$-calculus for generic $q$ is developed and related to the deformed oscillator of parameter $q^{1/2}$. By passing with care to the limit in which $q$ is a root of unity, one uncovers the full algebraic structure of ${{\cal…
We study the theory of representations of a multiparameter deformation of the function algebra of a simple algebraic group (as defined by Reshetikhin) when the quantum parameter is a root of unity. We extend the technics of De…
We examine some issues that arise in the q-deformation of a gauge theory. If the deformation is carried out by replacing the equal time commutators of free fields by the corresponding q-commutators, the resulting propagators are not very…
A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group…
A reducible representation of the Temperley-Lieb algebra is constructed on the tensor product of n-dimensional spaces. One obtains as a centraliser of this action a quantum algebra (a quasi-triangular Hopf algebra) U_q with a representation…
We investigate higher loop integrability for a q-deformation of the su(2)-sector of N=4 SYM theory. First we construct a generalisation of the long range spin chain, which for the lowest orders describes the non-deformed dilatation…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…
Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding…
We calculate the one-loop divergences for quantum gravity with cosmological constant, using new parametrization of quantum metric. The conformal factor of the metric is treated as an independent variable. As a result the theory possesses an…
A recent paper promises new constructions that may make it possible to achieve covariance in spherically symmetric models of loop quantum gravity. This claim is contrary to the discovery of several stubborn obstacles to covariance uncovered…
We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within $SU(2)$ quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering…
An approach for $q$-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
We review the main features of models where relativistic symmetries are deformed at the Planck scale. We cover the motivations and links to other quantum gravity approaches. We describe in some detail the most studied theoretical…
Given a scalar parameter $q$, the $q$-deformed Heisenberg algebra $\mathcal{H}(q)$ is the unital associative algebra with two generators $A,B$ that satisfy the $q$-deformed commutation relation $AB-qBA= I$, where $I$ is the multiplicative…
We introduce general q-deformed multiple polylogarithms which even in the dilogarithm case differ slightly from the deformation usually discussed in the literature. The merit of the deformation as suggested, here, is that q-deformed…
It is known that the involution corresponding to the compact form is incompatible with comultiplication for quantum groups at $|q|=1$. In this paper we consider the quantum algebra of functions on the deformed space $T^{*}G_{q}$ which…
Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commutation relation is shown to emerge in a natural way, when the deformation parameter is a root…
Quantum multiparameter deformation of real Clifford algebras is proposed. The corresponding irreducible representations are found.