kol (PowerPoint)

							                              Barak Kol
                  Hebrew University - Jerusalem
                        Jun 2011, Milos
               Outline
• set-up
• puzzles and previous work         Based on arXiv: 1103.5741 BK

• The new effective theory          W. Goldberger – early collaboration

• Results                           w/ M. Smolkin - related work
                       Set-up




Ultra relativistic (massless)
weak scattering
The parameters
Generalizations: Possible interactions, dimensions, masses
         Planckian scattering

• Intuitive condition for
  black hole creation
• Quantum black holes
      The perturbative regime
• The small parameter




• Objective:
  – trajectories and especially
  – scattering angle
                      Background
                        puzzles
• „t Hooft – natural probe
  for quantum gravity
- 4d Gravity simplifies for light-
   like
- reminiscent of 3d branch cuts
• w. Dray (1985) jump at shock
   wave
• (1987) Classical dominance
   including sub-planckian b!
• Relation with Veneziano
   amplitude
                     Background
                       puzzles
• Amati, Ciafaloni, Veneziano
   (1987,…,2008)
string theory as quant. Grav.
Eikonal approx, effective theory
 “H” correction diagram, dealing
   with IR div
• Verlinde2 (1992) –
   “topological field theory”
• Giddings
• Computer simulations
Choptuik-Pretorius 2009
Sperhake et al (2010)
 Post-Newtonian approximation
• Definition: relativistic correction to slow motion in
   flat space-time                       Damour, Blanchet, Schäfer

i.e. Mercury around the sun, binary system in
   adiabatic inspiral
• Small parameter v2/c2 ~GM/R <<1
• The EFT approach r0=2GM<<R               Goldberger, Rothstein
                                           (2004)
• The instantaneous
   spatial propagator
        Grav Field Re-definition
Stationary (t-independent)    Physical interpretation
  problem                       of fields
• Technically – KK
                              • Φ – Newtonian
  reduction over time
                                potential
• “Non-Relativistic
  Gravitation” - NRG fields   • A – Gravito-magnetic
  Non-linear definition         vector potential,
                                similar poles attract
                                                         0712.4116
                                                        BK, Smolkin
Recovering time dependence




                             1009.4116
                            BK, Smolkin
                       Non-orthonormal frame



                 1PN: 0712 Kol Smolkin
                 2PN: 0809 Gilmore Ross
                 3PN: 1104 Sturani-Foffa
Difficulty in importing PN ideas
  Each particle unperturbed motion is
  invariant under a different light-cone
             coordinate z+, z-.
Relation to other work presented at
            this meeting

• Holographic renormalization (Papadimitriou)

• Hydrodynamics and gravity (Y. Oz, A.
 Strominger, K. Skenderis)
 Related concepts




 Vought_V-173 “flying pancake”
experimental aircraft tested 1942-7
         Related concepts




Beat 1                  Beat 2                  Beat 3



         Mahler symphony no. 2, 3rd movement
               Conducted by L. Bernstein
         “St. Anthony Preaches to the Fishes”
The effective theory
  Recall the set-up..

    The action
                         Field lines
  • Imagine the field lines emanating from a point
    charge
  • At rest – spherical
  • When ultra relativistic
       – Lorentz contracted longitudinally
       – pancake-shaped transversely
       – Aichelburg-Sexl
  • “The particle carries
    a pancake on its nose”




“flying pancake”
         Sudden interaction
• The moment of passing – when the pancakes
  coincide
• Interaction localized in z,t

• Eq of motion are sudden,
  algebraic recursion
  rather than differential
                                     Mahler‟s 2nd
        The propagator




   2 k+ k- is a quadratic perturbation

The momentum transfer
           Field decomposition
• Dimensional reduction onto transverse space       BK 2010
  à la Kaluza-Klein




• Gab are (transverse) scalars. Analogous to the
  Newtonian potential.
  G++ couples to R, G-- couples to L.
• Aai are two (transverse) vectors.
  couple to mass current in the transverse plane.
• Spin is dipole charge for vectors.
                      Whole action
                                     BK (2011)
                                     Yoon (1996,99)




Extrinsic curvature




 deWitt metric
             Results
1st order and momentum transfer
     Ultra-relativistic dynamics
• “Light-cone”/ “infinite momentum frame”
• A particle has a total of 3 degrees of Dirac
                                           Weinberg
  freedom                                  Susskind

• 2 transverse (ordinary) degrees of
  freedom
• p+ plays the role of mass, z+ is time
• z- is a 1st order ODE – constraint – half dof
• e the world-line metric, or equiv z+ is the
  other half
       2-body effective action
                                                      Scalar interaction




For scalar→gravitational change e factors, add non-linear blik vertices
2nd order

      Mass shall




      Energy unchanged in CM frame
    Improved “renormalization”
• “Ordinary” initial conditions for scattering
  at t=-∞

• Specify initial conditions at nearest
  approach “t=0”
  pretending to know them.
Higher symmetry: parity in the pert theory
Evolve both forward and backward in time to
  eliminate the t=0 conditions
 Interaction duration – 3rd order
• Obtain a term of type




• ε2 c3/c1 estimates τ2, where τ is the (finite)
  duration
• We find τ≈ε b BK2011         At d=4 there is a pole in dim. Reg.

• This is consistent with the arc‟s radius of
  curvature being b,
  namely the center of force being at the other
  particle
                Discussion
• We defined a classical effective field theory
  (CLEFT) - different from PN.
• Result: interaction duration resolved
• Relation with eikonal approximation
Late 1960s, QFT context,
concept borrowed from optics –
 an approximation of wave optics calculated on the
  basis of rays
Eikon=image in greek
        Open questions
Non-conservation due to radiation:
Energy, momentum, angular momentum




        Cylon raider from Battlestar Galactica
  ΕΦΧΑΡΙΣΤΟ! Thank you!




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