Some comments on the universal constant in DSR

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 universal constant.Comment: 12 pages, Proceedings of DICE2006 (Piombino, Italy

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

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

And what if gravity is intrinsically quantic ?

Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, sting theory and quantum loop gravity are based on a quantum field theory - the latter is a quantum field theory of connections on a SU(2) group manifold and former a quantum field theory in two dimensional spaces. Here we argue that there is a very close relation between quantum mechanics and gravity. Without gravity quantum mechanics becomes ambiguous. We consider this observation as the evidence for an intrinsic relation between these fundamental laws of nature. We suggest a quantum role and definition for gravity in the context of a quantum universe, and present a preliminary formulation for gravity in a system with a finite number of particles.Comment: 8 pages, 1 figure. To appear in the proceedings of the DICE2008 conference, Castiglioncello, Tuscany, Italy, 22-26 Sep. 2008. V2: some typos remove

Field theories with homogenous momentum space

We discuss the construction of a scalar field theory with momentum space given by a coset. By introducing a generalized Fourier transform, we show how the dual scalar field theory actually lives in Snyder's space-time. As a side-product we identify a star product realization of Snyder's non-commutative space, but also the deformation of the Poincare symmetries necessary to have these symmetries realized in Snyder's space-time. A key feature of the construction is that the star product is non-associative.Comment: 9 pages, To appear in the Proceedings of the XXV Max Born Symposium, "The Planck Scale", Wroclaw, Poland, July 200