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The term higher gauge theory refers to the generalization of gauge theory to a theory of connections at two levels, essentially given by 1-and 2-forms. Geometrically, such a theory involves both the parallel transport of charged point particles along curves and the transport of line-like particles along surfaces. So far, there have been two approaches to… (More)
We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3d pure Euclidean gravity with cos-mological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF-theories. Moreover, we prove the invari-ance under more general conditions allowing the state sum to be… (More)
Left-right symmetric models are analyzed in the context of noncommutative geometry where we show that spontaneous parity violation is ruled out...
In this talk, we show how the Connes-Kreimer Hopf algebra morphism can be extended when taking into account the wave-function renormalization. This leads us to a semi-direct product of invertible power series by formal diffeomorphisms. 1 The Connes-Kreimer formalism As has already been mentioned by A. Connes in his lecture , the standard BPHZ recur-sion… (More)
This paper aims at presenting the first steps towards a formulation of the Exact Renorma-lization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated… (More)
We present a scheme to study non-Abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against decoherence. We pinpoint the sources of error that must be corrected to achieve a geometric implementation of quantum computation completely resilient to Markovian… (More)
From the Physics point of view, time is now best described through General Relativity, as part of space-time which is a dynamical object encoding gravity. Time possesses also some intrinsic irreversibility due to thermodynamics, quantum mechanical effects... This irreversibility can look puzzling since time-like loops (and hence time machines) can appear in… (More)
Deformed Special Relativity is usually presented as a deformation of Special Relativity accommodating a new universal constant, the Planck mass, while respecting the relativity principle. In order to avoid some fundamental problems (e.g. soccer ball problem), we argue that we should switch point of view and consider instead the Newton constant G as the… (More)
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 undergoes an unavoidable measurement ''back-action'' that modifies its properties. In a quantum-gravitational setting, it… (More)
We discuss a toy model for an emergent non-relativistic gravitational theory. Within a certain class of Bose–Einstein condensates, it is possible to show that, in a suitable regime, a modified version of non-relativistic Newtonian gravity does effectively describes the low energy dynamics of the coupled system condensate/quasi-particles.