Tests of Lorentz invariance: a 2013 update

TL;DR

This paper reviews and updates tests of Lorentz invariance within effective field theories, discussing theoretical frameworks, experimental constraints, and specific cases like the OPERA anomaly and Hořava-Lifshitz gravity.

Contribution

It provides a comprehensive update on Lorentz invariance tests, including theoretical derivations, constraints on LIV parameters, and analysis of specific quantum gravity scenarios.

Findings

Constraints on Lorentz-violating parameters in EFT

Analysis of OPERA anomaly as a LIV test case

Implications of Hořava-Lifshitz gravity for LIV

Abstract

We present an updated review of Lorentz invariance tests in Effective field theories (EFT) in the matter as well as in the gravity sector. After a general discussion of the role of Lorentz invariance and a derivation of its transformations along the so called von Ignatovski theorem, we present the dynamical frameworks developed within local EFT and the available constraints on the parameters governing the Lorentz breaking effects. In the end, we discuss two specific examples, the OPERA "affaire" and the case of Ho\v{r}ava-Lifshitz gravity. The first case will serve as an example, and a caveat, of the practical application of the general techniques developed for constraining Lorentz invariance violation (LIV) to a direct observation potentially showing these effects. The second case will show how the application of the same techniques to a specific quantum gravity scenario has far fetching implications not foreseeable in a purely phenomenological EFT approach.