Abstract
We study particle dynamics in a space-time invariant under the $DISIM_b(2)$ group - the deformation of the $ISIM(2)$ symmetry group of very special relativity. We find that the Lorentz violation leads to the creation of higher order (hidden) symmetries which are connected to those broken at the space-time level. Through the perspective of the conserved quantities of the special relativistic case the Lorentz violation is linked to specific non-commutative relations in phase-space.
Highlights
The subject of Lorentz violation has a long history in theoretical physics and is motivated by different arguments in a broad spectrum of theories
We are interested in the symmetry structure of the particle dynamics in the deformed version of very special relativity (VSR), which incorporates such a violation
We reveal the existence of higher order symmetries, which are connected to breaking Lorentz invariance
Summary
The subject of Lorentz violation has a long history in theoretical physics and is motivated by different arguments in a broad spectrum of theories (string theory, loop quantum gravity, noncommutative geometry, etc. [1,2,3,4]). We are interested in the symmetry structure of the particle dynamics in the deformed version of very special relativity (VSR), which incorporates such a violation. In this context, we reveal the existence of higher order symmetries, which are connected to breaking Lorentz invariance. The Bogoslovsky-Finsler line element (1) belongs to this class, and even though it has a distinct symmetry structure compared to the g of (2), it has its extrema exactly on the same trajectories as the latter This very interesting property is the motive of this work.
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