Abstract
We present new results for classical-particle propagation subject to Lorentz violation. Our analysis is dedicated to spin-nondegenerate operators of arbitrary mass dimension provided by the fermion sector of the Standard-Model Extension. In particular, classical Lagrangians are obtained for the operators $\hat{b}_{\mu}$ and $\hat{H}_{\mu\nu}$ as perturbative expansions in Lorentz violation. The functional dependence of the higher-order contributions in the background fields is found to be quite peculiar, which is probably attributed to particle spin playing an essential role for these cases. This paper closes one of the last gaps in understanding classical-particle propagation in the presence of Lorentz violation. Lagrangians of the kind presented will turn out to be valuable for describing particle propagation in curved backgrounds with diffeomorphism invariance and/or local Lorentz symmetry explicitly violated.
Highlights
Theories of physics at the Planck scale such as strings [1], loop quantum gravity [2], noncommutative spacetime structures [3], and spacetime foam [4] as well as nontrivial spacetime topologies [5] and Horava-Lifshitz gravity [6] predict violations of Lorentz invariance
To be able to translate the absence of signals for Lorentz violation into constraints on meaningful physical quantities, the Standard-Model extension (SME) was constructed [7,8] as an effective field theory framework that parametrizes deviations from Lorentz symmetry
There are certain types of Lorentz violation that cannot be observed in Minkowski spacetime even if they are enormous, as they can be removed from the Lagrange density by a redefinition of the physical fields
Summary
Theories of physics at the Planck scale such as strings [1], loop quantum gravity [2], noncommutative spacetime structures [3], and spacetime foam [4] as well as nontrivial spacetime topologies [5] and Horava-Lifshitz gravity [6] predict violations of Lorentz invariance. There are certain types of Lorentz violation that cannot be observed in Minkowski spacetime even if they are enormous, as they can be removed from the Lagrange density by a redefinition of the physical fields Such a redefinition loses its validity in the presence of gravity, whereupon the enormous value would be suppressed by the weakness of the gravitational interaction [18]. Results for nonminimal spin-nondegenerate operators at first order in Lorentz violation are already available [27], nothing is known about the structure of higher-order contributions. This gap shall be closed with the current article. Natural units will be used with ħ 1⁄4 c 1⁄4 1 unless otherwise stated
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