Florian Girelli 2. General construction of DSR 3. Exploring the physics of DSR 1. DSR: phenomenology of QG

QUANTUM GRAVITY String Theory Causal Sets Loop Quantum Gravity

Philosophy behind DSR  Instead of deriving a semi classical limit of the Quantum Gravity Theory, derive an effective theory from a well known theory: Special Relativity.  To this aim one introduces characteristic scales of Quantum Gravity:  One has to modify the symmetries in order to accommodate these new constants. Special Relativity is the first example of such process (cf talk by Chryssomalis earlier).  Physics of DSR should be different than relativistic physics, as much as relativistic physics is different than newtonian physics.  The resulting theory should describe a low energy phenomenology, directly testable mainly in astrophysical context (gamma ray, cosmic rays).

Special Relativity as an inspiration  Let us take the Schwarzschild ratio:  For spherical bodies (of radius L ) of rest mass M, we always need: We would like to incorporate this “new” universal constant in the relativistic context: incorporate a feature of gravity, without having gravity.  This is remnant of Special Relativity: we have a maximum length per unit of time.

Let Special Relativity guide us!  To implement a maximum speed in Special Relativity we modify the space of speeds into an hyperboloid.  The addition of the speeds is then modified! Indeed we want that the sum of speeds to be still smaller than the speed of light.

 On the configuration space, we have the notion of space-time that appears.  We have the relativistic speed such that  Physical objects are given in terms of linear representations of the Poincare group ISO(3,1).

Let’s do the same with momentum now!  We are going to implement a maximum rest mass, we choose the Planck mass,.  We define a DSR momentum, The relativistic momentum is now defined as We have therefore now a momentum which rest mass is bounded by the Planck mass.

 Addition of momenta is on the de Sitter space: the rest mass is always bounded. If we define the addition in this way, we run in the soccer ball problem: the cutoff is not renormalized.  To recover additive quantities one needs to get to the Poincare-de Sitter group ISO(4,1).  Addition of the pentamomenta naturally implies a renormalization of the maximum mass: maximum mass is the 5 dimensional mass.  There exists other coordinate systems: physical interpretation is different, as a different quantity is bounded. Bicrossproduct basis: 3-momentum is bounded, with associative addition of relativistic momenta. Bicrossproduct basis: 3-momentum is bounded, with associative addition of relativistic momenta. Magueijo-Smolin basis: Energy is bounded, with addition of momenta highly non associative.

What about space-time?? There exists different approaches to reconstruct space time: 1.5d approach: space-time-mass (already introduced by Wesson) and its variants. 2.4d approach: 1.Coordinates as tangent vectors (Snyder’s approach, but also in the Minkowski space.) 2.Rainbow metric (Magueijo’s approach). This approach can be seen as 4d projection of the 5d construction.

Physics is about dynamics  By specifying some dynamics we should be able to eliminate some possibilities, in particular make also the distinction between 4d and 5d.  4d case: –Inertial observer: Casimir of the (deformed) symmetry: –Uniformly accelerated observer (work in progress): A massive body seems to reach the speed of light (in the Magueijo-Smolin setting)….

 5d case (work in progress):  The new physics is hidden in the fifth dimension sector, but very tiny physics This has to be deepened…

Conclusions  I recalled the general construction for DSR, and showed the parallel with Special Relativity.  I mentioned the main problems of DSR: the many bodies state (soccer ball problem) and the interpretation of dynamics.  I argued that a 5d approach should provide a better angle of attack to make a consistent theoretical framework.  DSR is extremely interesting: –Very close to Special Relativity –It can be related to the Space-Time-Mass introduced by Wesson: A non compactified Kaluza-Klein theory, where the extra dimension is the “mass”. This theory has been developed in the astrophysical and cosmological context and is still consistent with observations.  Most exciting: the field theory approach hasn’t been developed yet –It should provide a cutoff consistent with symmetries: natural regularization –It must be related to Percacci’s approach –Then potential relation with Randall-Sundrum model.