Related papers: On positive definiteness over locally compact quan…

We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…

We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural…

A natural scheme is established for the approximation of quantum Levy processes on locally compact quantum groups by quantum random walks. We work in the somewhat broader context of discrete approximations of completely positive quantum…

We extend the construction of generalized fixed point algebras to the setting of locally compact quantum groups - in the sense of Kustermans and Vaes - following the treatment of Marc Rieffel, Ruy Exel and Ralf Meyer in the group case. We…

We give a partial solution to a long-standing open problem in the theory of quantum groups, namely we prove that all finite-dimensional representations of a wide class of locally compact quantum groups factor through matrix quantum groups…

We first note that, at least in perturbation theory, there is a well-defined (subject to regularization) Lorentzian definition of the quantum effective action in both flat and curved space including (perturbative) gravity. The advantage of…

We introduce a non commutative analog of the Bohr compactification. Starting from a general quantum group G we define a compact quantum group bG which has a universal property such as the universal property of the classical Bohr…

In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…

Kolmogorov decomposition for a given completely positive definite kernel is a generalization of Paschke's GNS construction for the completely positive map. Using Kolmogorov decomposition, to every quantum dynamical semigroup (QDS) for…

We generalize the concept of stabilizer subgroups to compact quantum groups.

This article proves the existence of completely positive quasimultiplicative maps from the group algebra of imprimitive reflection groups to the set of bounded operators, and uses those linear maps to define creation and annihilation…

We establish several sufficient conditions under which a locally integrable function $f:\mathbb R^n \to \mathbb R$ represents a positive-definite distribution. In particular we consider functions of the form $f(\|x\|)$ where $\|\cdot\|$ is…

We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed…

We present a discussion on local quantum correlations and their relations with entanglement. We prove that vanishing coefficient of quantum correlations implies separability. The new results on locally decomposable maps which we obtain in…

We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…

Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…

For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a…

We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

In this article, part of the author's thesis, we propose a definition for measured quantum groupoid. The aim is the construction of objects with duality including both quantum groups and groupoids. We base ourselves on J. Kustermans and S.…

We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…