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Weak Ultra Relativistic Scattering

Weak Ultra Relativistic Scattering. Barak Kol Hebrew University - Jerusalem Jun 2011, Milos. Outline set-up puzzles and previous work The new effective theory Results. Based on arXiv: 1103.5741 BK W. Goldberger – early collaboration w/ M. Smolkin - related work. Set-up.

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Weak Ultra Relativistic Scattering

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  1. Weak Ultra Relativistic Scattering Barak Kol Hebrew University - Jerusalem Jun 2011, Milos • Outline • set-up • puzzles and previous work • The new effective theory • Results Based on arXiv: 1103.5741 BK W. Goldberger – early collaboration w/ M. Smolkin - related work

  2. Set-up Ultra relativistic (massless) weak scattering The parameters Generalizations: Possible interactions, dimensions, masses

  3. Intuitive condition for black hole creation Quantum black holes Planckian scattering

  4. The small parameter Objective: trajectories and especially scattering angle The perturbative regime

  5. ‘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 Backgroundpuzzles

  6. 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) Backgroundpuzzles

  7. Post-Newtonian approximation • Definition: relativistic correction to slow motion in flat space-time i.e. Mercury around the sun, binary system in adiabatic inspiral • Small parameter v2/c2 ~GM/R <<1 • The EFT approach r0=2GM<<R • The instantaneous spatial propagator Damour, Blanchet, Schäfer Goldberger, Rothstein (2004)

  8. Stationary (t-independent) problem Technically – KK reduction over time “Non-Relativistic Gravitation” - NRG fields Non-linear definition Physical interpretation of fields Φ – Newtonian potential A – Gravito-magnetic vector potential, similar poles attract Grav Field Re-definition 0712.4116 BK, Smolkin

  9. Recovering time dependence 1009.4116 BK, Smolkin Non-orthonormal frame 1PN: 0712 Kol Smolkin 2PN: 0809 Gilmore Ross 3PN: 1104 Sturani-Foffa

  10. Difficulty in importing PN ideas Each particle unperturbed motion is invariant under a different light-cone coordinate z+, z-.

  11. Relation to other work presented at this meeting • Holographic renormalization (Papadimitriou) • Hydrodynamics and gravity (Y. Oz, A. Strominger, K. Skenderis)

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

  13. Beat 3 Beat 2 Related concepts Beat 1 Mahler symphony no. 2, 3rd movement Conducted by L. Bernstein “St. Anthony Preaches to the Fishes”

  14. The effective theory Recall the set-up.. The action

  15. “flying pancake” 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”

  16. 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 Sudden interaction

  17. 2 k+ k- is a quadratic perturbation The momentum transfer The propagator

  18. Dimensional reduction onto transverse space à la Kaluza-Klein Gab are (transverse) scalars. Analogous to the Newtonian potential. G++ couples to R, G-- couples to L. Aaiare two (transverse) vectors. couple to mass current in the transverse plane. Spin is dipole charge for vectors. Field decomposition BK 2010

  19. Whole action BK (2011) Yoon (1996,99) Extrinsic curvature deWitt metric

  20. Results1st order and momentum transfer

  21. Ultra-relativistic dynamics • “Light-cone”/ “infinite momentum frame” • A particle has a total of 3 degrees of freedom • 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 Dirac Weinberg Susskind

  22. 2-body effective action Scalar interaction For scalar→gravitational change e factors, add non-linear blik vertices

  23. 2nd order Mass shall Energy unchanged in CM frame

  24. 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

  25. Obtain a term of type ε2 c3/c1 estimates τ2, where τ is the (finite) duration We find τ≈ε b This is consistent with the arc’s radius of curvature being b, namely the center of force being at the other particle Interaction duration – 3rd order At d=4 there is a pole in dim. Reg. BK2011

  26. 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

  27. Cylon raider from Battlestar Galactica Open questions Non-conservation due to radiation: Energy, momentum, angular momentum

  28. ΕΦΧΑΡΙΣΤΟ! Thank you! Darkness and Light in our region

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