48 research outputs found
Deformed symmetries from quantum relational observables
Deformed Special Relativity (DSR) is a candidate phenomenological theory to describe the Quantum Gravitational (QG) semi-classical regime. A possible interpretation of DSR can be derived from the notion of deformed reference frame. Observables in (quantum) General Relativity can be constructed from (quantum) reference frame – a physical observable is then a relation between a system of interest and the reference frame. We present a toy model and study an example of such quantum relational observables. We show how the intrinsic quantum nature of the reference frame naturally leads to a deformation of the symmetries, comforting DSR to be a good candidate to describe the QG semi-classical regime
Non-Commutativity of Effective Space-Time Coordinates and the Minimal Length
Considering that a position measurement can effectively involve a
momentum-dependent shift and rescaling of the "true" space-time coordinates, we
construct a set of effective space-time coordinates which are naturally
non-commutative. They lead to a minimum length and are shown to be related to
Snyder's coordinates and the five-dimensional formulation of Deformed Special
Relativity. This effective approach then provides a natural physical
interpretation for both the extra fifth dimension and the deformed momenta
appearing in this context.Comment: 5 page
Scalar field theory in Snyder space-time: alternatives
We construct two types of scalar field theory on Snyder space-time. The first
one is based on the natural momenta addition inherent to the coset momentum
space. This construction uncovers a non-associative deformation of the
Poincar\'e symmetries. The second one considers Snyder space-time as a subspace
of a larger non-commutative space. We discuss different possibilities to
restrict the extra-dimensional scalar field theory to a theory living only on
Sndyer space-time and present the consequences of these restrictions on the
Poincar\'e symmetries. We show moreover how the non-associative approach and
the Doplicher-Fredenhagen-Roberts space can be seen as specific approximations
of the extra-dimensional theory. These results are obtained for the 3d
Euclidian Snyder space-time constructed from \SO(3,1)/\SO(3), but our results
extend to any dimension and signature.Comment: 24 pages
Physics of Deformed Special Relativity
In many different ways, Deformed Special Relativity (DSR) has been argued to
provide an effective limit of quantum gravity in almost-flat regime.
Unfortunately DSR is up to now plagued by many conceptual problems (in
particular how it describes macroscopic objects) which forbids a definitive
physical interpretation and clear predictions. Here we propose a consistent
framework to interpret DSR. We extend the principle of relativity: the same way
that Special Relativity showed us that the definition of a reference frame
requires to specify its speed, we show that DSR implies that we must also take
into account its mass. We further advocate a 5-dimensional point of view on DSR
physics and the extension of the kinematical symmetry from the Poincare group
to the Poincare-de Sitter group (ISO(4,1)). This leads us to introduce the
concept of a pentamomentum and to take into account the renormalization of the
DSR deformation parameter kappa. This allows the resolution of the "soccer ball
problem" (definition of many-particle-states) and provides a physical
interpretation of the non-commutativity and non-associativity of the addition
the relativistic quadrimomentum.Comment: 8 pages, short version of gr-qc/0412004, Proceedings of the Second
International Workshop DICE2004 (Castello di Piombino, Tuscany) "From
Decoherence and Emergent Classicality to Emergent Quantum Mechanics
Emergent gravitational dynamics in Bose-Einstein condensates
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.Comment: 9 pages. To appear in the Proceedings of the XXV Max Born Symposium,
"The Planck Scale", Wroclaw, Poland, July 200
Wave-Function renormalization and the Hopf algebra of Connes and Kreimer
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.Comment: 5 pages, no figure, talk presented in the conference "Brane New World
and Noncommutative Geometry", Torino, Villa Gualino,(Italy) Octobe