Florian Girelli

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• Towards a 5d approach
• of
• Deformed Special Relativity

• Florian Girelli

1. DSR phenomenology of QG
2. General construction of DSR
3. Exploring the physics of DSR
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QUANTUM GRAVITY
Loop Quantum Gravity
Causal Sets
String Theory
One should try to make predictions for
experiments!
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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).

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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.

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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.

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• 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).

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Lets 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.

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• 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.
• Magueijo-Smolin basis Energy is bounded, with
  addition of momenta highly non associative.

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What about space-time??

• There exists different approaches to reconstruct
  space time
• 5d approach space-time-mass (already introduced
  by Wesson) and its variants.
• 4d approach
• Coordinates as tangent vectors (Snyders
  approach, but also in the Minkowski space.)
• Rainbow metric (Magueijos approach). This
  approach can be seen as 4d projection of the 5d
  construction.

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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).

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

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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 hasnt
  been developed yet
• It should provide a cutoff consistent with
  symmetries natural regularization
• It must be related to Percaccis approach
• Then potential relation with Randall-Sundrum
  model.