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SpiffyKavu
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IUCSS Summer School on the Lorentz- and CPT-violating Standard Model Extension (SME)
This program is going on now, at Indiana University. The title pretty much covers what the school is about. The SME simply takes the ordinary standard model and adds terms to the Lagrangian which violate Lorentz symmetry essentially by adding in a preferred direction via vectors and general tensors. Notes are being posted more-or-less daily at the program website.
Of course, there are an infinite number of possible terms, so most people just consider specific terms or the minimal SME, which adds only those terms which are power-counting renormalizable and gauge symmetric (under the full Standard Model gauge symmetry), along with a couple other assumptions. More more generic terms can be added, and some of these (non-power-counting renormalizable) operators have constraints on them from experiment.
It does not claim to be any fundamental theory. Rather, it only claims to construct a generalized effective theory of Lorentz violation which encompasses known physics, so these vectors and tensors added in must have small coefficients.
The most stringent bounds have so far come from astrophysical tests of the CMB and gamma-ray bursts, but other systems have been analyzed, from atomic clocks to resonant cavities to meson oscillations signals at our particle accelerators.
I must add that some incarnations of the SME DO include gravity, which has its own Lorentz violating terms added on as well. As might be expected, any treatment with non-flat backgrounds, and especially dynamical background geometry, must be a classical treatment. This means to me that the SME with gravity cannot test weak/strong interactions, only gravitational and electromagnetic.
I am slowly typing up the notes I have been taking, but the presenter's presentations are also being posted. I'm also a 2nd year grad student doing observational gamma-ray astronomy, so my notes are likely incorrect in places and certainly incomplete. We'd all, of course, love to be able to have a fundamental theory which includes both gravity and the standard model which can give us a specific low-energy effective theory, but no such model exists today, so people are somewhat content with studying all possible terms.
As a note, you might have noticed I haven't really said anything about CPT violation outside of the title. At the level of the Lagrangian, it seems that CPT violation implies Lorentz violation for local theories (Greenberg 2002 [arxiv version]).
This program is going on now, at Indiana University. The title pretty much covers what the school is about. The SME simply takes the ordinary standard model and adds terms to the Lagrangian which violate Lorentz symmetry essentially by adding in a preferred direction via vectors and general tensors. Notes are being posted more-or-less daily at the program website.
Of course, there are an infinite number of possible terms, so most people just consider specific terms or the minimal SME, which adds only those terms which are power-counting renormalizable and gauge symmetric (under the full Standard Model gauge symmetry), along with a couple other assumptions. More more generic terms can be added, and some of these (non-power-counting renormalizable) operators have constraints on them from experiment.
It does not claim to be any fundamental theory. Rather, it only claims to construct a generalized effective theory of Lorentz violation which encompasses known physics, so these vectors and tensors added in must have small coefficients.
The most stringent bounds have so far come from astrophysical tests of the CMB and gamma-ray bursts, but other systems have been analyzed, from atomic clocks to resonant cavities to meson oscillations signals at our particle accelerators.
I must add that some incarnations of the SME DO include gravity, which has its own Lorentz violating terms added on as well. As might be expected, any treatment with non-flat backgrounds, and especially dynamical background geometry, must be a classical treatment. This means to me that the SME with gravity cannot test weak/strong interactions, only gravitational and electromagnetic.
I am slowly typing up the notes I have been taking, but the presenter's presentations are also being posted. I'm also a 2nd year grad student doing observational gamma-ray astronomy, so my notes are likely incorrect in places and certainly incomplete. We'd all, of course, love to be able to have a fundamental theory which includes both gravity and the standard model which can give us a specific low-energy effective theory, but no such model exists today, so people are somewhat content with studying all possible terms.
As a note, you might have noticed I haven't really said anything about CPT violation outside of the title. At the level of the Lagrangian, it seems that CPT violation implies Lorentz violation for local theories (Greenberg 2002 [arxiv version]).