1. recently renewed interest
Many approaches
Will focus on the approach our group has taken

2. A. Motivations Physics is an experimental science
 laws must be tested with increasing quality
(2) Discovery potential: various approaches to underlying
physics can accommodate minuscule departures from
Lorentz symmetry in the ground state
- bottom-up motivation
- top-down motivation

3. bottom-up motivation: What can be measured with Planck
precision? Is there a corresponding quantum-gravity effect?
Symmetries:
- allow exact theoretical prediction
- are typically amenable to ultrahigh-precision (null) tests
Tests of spacetime symmetries
could probe Planck-scale physics
Quantum gravity: likely to affect spacetime structure
- More than 4 dimensions?
- Non-commuting coordinates?
- Discreteness?
- “Foamy” structure? …

4. Top-down motivation:
String field theory (Kostelecký, Potting et al ‘98)
nontrivial vacuum through VEV of tensor
Spacetime foam (Ellis et al ‘98)
nontrivial vacuum through virtual black holes
Nontrivial spacetime topology (Klinkhamer ‘00)
nontrivial vacuum via compact conventional dim.
Loop quantum gravity (Alfaro et al ‘00)
nontrivial vacuum via choice of spin-network state
Noncommutative geometry (Carroll et al ‘01)
nontrivial vacuum through fixed ~ [x, x]
Varying scalars (Kostelecký et al ‘03)
nontrivial vacuum through gradient of scalar
. . .

5. B. Low-energy EFT for Lorentz/CPT violation - the SME
- k, s, ... coefficients for Lorentz violation
- minimal SME  fermion 44, photon 23, ...
- amenable to ultrahigh-precision tests (Sec C)
- generated by underlying physics (Sec A)
Colladay, Kostelecký ‘97;’98; Kostelecký ‘04; Coleman, Glashow ‘99
Remarks:
- can consider higher-dim. operators
(Myers, Pospelov ‘03; Reyes, Urrutia, Vergara ‘07; ‘08)
- can consider spacetime dependence, e.g., s~ R, etc.
(Shore ‘02; ‘03; ‘04; ‘07; ‘08; Sudarsky et al. ‘05; ‘08)

6. sample theoretical investigations of the SME
- radiative corrections (Jackiw, Kostelecký '99, next talk)
- causality and stability (Kostelecký, R.L. '01)
- gravity: LV must be dynamical (e.g., spontaneous) (Kostelecký '04)
- NG modes from SSB  theory of gravity (last talk today)
- supersymmetry (Berger, Kostelecký '02)
- "Anti-CPT Theorem" (Greenberg '02)
- one-loop renormalizability (Kostelecký, Lane, Pickering '02)
- dispersion relations and kinematical analyses (R.L. '03)
- generalization of conventional math. formulas (R.L. '04; '06)
- symmetry studies (Cohen, Glashow '06; Hariton, R.L. '07)

7. One-flavor QED limit of the SME Lagrangian:
where
Least constrained coefficient in QED: one component of k
- non-birefr. compnts : 1 isotropic parameter tr
- birefringent components: exp. constrained at the level
 will be dropped from analysis
- tr is only bounded at the 10-8 level by experiments
 will focus on tr in what follows

8. C. Experimental searches for tr
 need physical effects of tr
example: dispersion relation
intuitively: refractive index of the vacuum
tr > 0 light is slower rel. to conventional case
tr < 0 light is faster rel. to conventional case
each case has its individual phenomenology
 the 2 cases need to be studied separately

9. Analogy: conventional medium (e.g., crystal) with n > 1
(a) the casetr > 0
Analogy: conventional medium (e.g., crystal) with n > 1
also slows down light
A high-speed charge (vq > c/n)
in such a medium rapidly
loses energy through emission
of Cherenkov light.
Expectation: tr > 0 would lead to similar instabilities in a Lorentz-violating vacuum  “vacuum Cherenkov radiation”

10. Vacuum-Cherenkov threshold for casetr > 0:
4-momentum conservation with modified photon disp. rel.:
electrons with energies above
should emit Cherenkov photons
but this effect is not seen for electrons
with energies Ee = GeV at LEP, so

11. Cherenkov-radiation rate for tr:
Example: - LEP electrons at Ee=104.5 GeV,
- threshold Ethres 1% below Ee
 would fall below threshold within 23cm
 in this case, the effect is extremely efficient

12. (b) the casetr < 0 instead of electrons, photons are unstable:
photons with energies above
would decay
but this effect is not seen for photons with
energies E = 300 GeV at the Tevatron, so

13. Photon-decay rate for tr:
Example: - Tevatron photons at E= 300 GeV,
- threshold Ethres 1% below E
 would decay within 15m
 in this case, the effect is extremely efficient

14. Alternative bound with synchrotron radiation:
ordinary physics: accelerated charges radiate
 circular motion causes synchrotron losses

15. tr Lorentz violation would modify synchrotron losses:
at LEP, synchrotron losses were accurately determined:
This yields the best current bound:

16. Other phenomenological studies performed within SME
Hydrogen and Antihydrogen spectroscopy
Bluhm, Kostelecký, Russell '99
Phillips et al. '01
Penning-Trap experiments
Bluhm, Kostelecký, Russell '97; '98
Gabrielse et al. '99
Mittelman et al. '99
Dehmelt et al. '99
Studies of muons
Bluhm, Kostelecký, Lane '99
Hughes et al. '00
(g-2) collaboration ‘08
Clock-comparison tests
Kostelecký, Lane '99
Hunter et al. '99
Stoner '99
Bear et al. '00
Cane et al. ‘04

17. Satellite-based tests Kostelecký et al. '02; '03 ACES PARCS? RACE?
SUMO?
OPTIS
Tests involving photons and radiative effects (see also next talk)
Carroll, Field, Jackiw '90
Colladay, Kostelecký '98
Jackiw, Kostelecký '99
Kostelecký, Mewes '01; '02; ‘06; ‘07
Lämmerzahl et al. '03
Lipa et al. '03
Stanwix et al. '05
Klinkhamer et al. '07
Gravity
Bailey, Kostelecký '06
Battat et al. ‘07
Müller et al. ‘08

18. Studies of baryogenesis (see also J. Alfaro’s talk tomorrow)
Bertolami et al. '97
Studies of neutrinos
Barger, Pakvasa, Weiler, Whisnant '00
Kostelecký et al. '03; '04
Katori et al. '06
Barger, Marfatia, Whisnant ‘07
Kinematical studies of cosmic rays
Coleman, Glashow '99
Bertolami, Carvalho '00
R.L. '03
Altschul ‘06; ‘07
Studies of neutral-meson systems
Kostelecký et al. '95; '96; '98; '00
KTeV Collaboration, Hsiung et al. '99
FOCUS Collaboration, Link et al. '03
OPAL Collaboration, Ackerstaff et al. '97
DELPHI Collaboration, Feindt et al. '97
BELLE Collaboration
BaBar Collaboration ‘08

19. D. Summary (1) various theoretical approaches to
presently no credible exp. evidence for Relativity violations, but:
(1) various theoretical approaches to
quantum gravity can cause such violations ?
(2) at low E, such violations are
described by SME test framework
(eff. field theory + background fields) 
Meine Forschung: Bindeglied zwischen QG und Exp.
(3) high-precision tests at,
e.g., colliders are possible