6 ms·

Lorentz symmetry is associated with conservation of center of mass, see [1] (Note that it's actually talking about Lorentz symmetry without rotations (called "

• raattgift 10y ago
  That's true for the Lagrangian written down in the excellent answer at stackexchange, but the equivalent Lagrangian of the Standard Model Extension (SME) (which is what is the topic of the Bourgoin et al. paper) is filled with additional terms. For example, a minimal SME photon Lagrangian is developed in section II. A. of Kostelcky and Mewes @ https://arxiv.org/abs/0905.0031 https://arxiv.org/abs/0905.0031 The difference between a minimal SME (mSME) and the full SME is that the latter admits terms of any mass dimension greater than two, while mSME requires power-counting renormalizability (in order to be an effective field theory) so mSME admits only terms of dimension four. As a result mSME can only have a finite number of Lorentz invariance violation parameters, while SME can have an infinite number of them. The bright side is that mSME can represent locally the Lagrangian in the physics.se answer you link to with a fixing of parameters; the dim side is that in general one does not want to do this a priori, precisely because the mSME is a tool to investigate whether the Lorentz SO(3,1; R) group is an exact feature of nature at every point, rather than postulating that it is (as the Standard Model does, and indeed as Special Relativity and General Relativity do). For example, SME is useful for dealing with things like this: https://www.wikiwand.com/en/Bumblebee_models#/Lagrangian https://www.wikiwand.com/en/Bumblebee_models#/Lagrangian where the non-matter term might not reduce (via GL(4, R)) to the groupoid of local coordinate transforms on the manifold and the local SO(3, 1; R) Lorentz group on the orthonormal frames (tetrad formalism) which are the symmetries of General Relativity. The point is to find out under what conditions any such model does vary from General Relativity. (We already have a good EFT for GR itself, and the result of the Bourgoin et al. paper is that it remains good.)
  • raattgift 10y ago
    Half-jokingly one could say that what's conserved under the transformations of Lorentz group of the SME is the behaviour of the Standard Model under changes to the physics of gravity. A bit less jokingly, that corresponds fairly well to conserving the microscopic description of the centre of mass-energy-momentum rather than just the centre of mass-energy-momentum (at t=0 for some total energy) as in phys.se answer in the GP comment.