weak ultra relativistic scattering
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Barak KolHebrew 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
Ultra relativistic (massless) weak scatteringThe parametersGeneralizations: 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
: 1cmGE
b
Backgroundpuzzles
• ‘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
• 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 simulationsChoptuik-Pretorius 2009Sperhake et al (2010)
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
2 2 2 20
1 1 1
k k k k
0T R k k
Goldberger, Rothstein(2004)
Grav Field Re-definitionStationary (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
0712.4116BK, Smolkin
2 2 / 32 2
2 2 22 13 4 3
2
, ,
1exp
16
i
d
ij
ii i j
ddd
ij
d
h
ds e dt dx e dx dx
S dt dx RG
A
A
F
Recovering time dependence
1009.4116BK, Smolkin
Non-orthonormal frame
1PN: 0712 Kol Smolkin2PN: 0809 Gilmore Ross3PN: 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 movementConducted by L. Bernstein
“St. Anthony Preaches to the Fishes”
The effective theory
4
,
1; , [ ]
16
, /2
A A AA R L
I
A A A
S g X e d x R g SG
pS X e ds g X X X e
Recall the set-up..
The action
Field lines
“flying pancake”
• 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”
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
k k k
~ 1cmG Ek
k b
2 2 2
1 1 1
2k k k k k
2cmp G E k
Field decomposition
• 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.
• Aai are two (transverse) vectors.
couple to mass current in the transverse plane.• Spin is dipole charge for vectors.
2
, , , , , , ,
( )( )
aab i ij
a ba
ab i j ij
i b j i j
g a b i j x y
ds dz dx dz dx
G A g
G A A xg d dx
BK 2010
Whole action
Extrinsic curvature
deWitt metric
BK (2011)Yoon (1996,99)
Results1st order and momentum transfer
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
DiracWeinbergSusskind
2-body effective actionScalar 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 theoryEvolve 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• This is consistent with the arc’s radius of
curvature being b, namely the center of force being at the other particle
31 3 ''p c s sc
BK2011 At d=4 there is a pole in dim. Reg.
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
Darkness and Light in our region
ΕΦΧΑΡΙΣΤΟ! Thank you!