57 research outputs found
Snyder Space-Time: K-Loop and Lie Triple System
Different deformations of the Poincare symmetries have been identified for
various non-commutative spaces (e.g. -Minkowski, , Moyal). We
present here the deformation of the Poincare symmetries related to Snyder
space-time. The notions of smooth "K-loop", a non-associative generalization of
Abelian Lie groups, and its infinitesimal counterpart given by the Lie triple
system are the key objects in the construction
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
Physics of Deformed Special Relativity: Relativity Principle revisited
In many different ways, Deformed Special Relativity (DSR) has been argued to
provide an effective limit of quantum gravity in almost-flat regime. Some
experiments will soon be able to test some low energy effects of quantum
gravity, and DSR is a very promising candidate to describe these latter.
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. In particular, the coproduct of the
kappa-Poincare algebra is interpreted as defining the law of change of
reference frames and not the law of scattering. This point of view places DSR
as a theory, half-way between Special Relativity and General Relativity,
effectively implementing the Schwarzschild mass bound in a flat relativistic
context.Comment: 24 pages, Revtex
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
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
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
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