As evidenced by this meeting, there is a growing feeling that Lorentz invariance should be questioned and tested. Tentative results from from quantum gravity and string theory hint that the ground state may not be Lorentz invariant, and new techniques are allowing for experiments with unprecedented precision and astrophysical observations at unprecedented high energies. Moreover, due to the unb...

In these notes we study Lorentz transformations and focus on the group of proper, orthochronous Lorentz transformations, donated by L+. (These Lorentz transformations have determinant one and preserve the direction of time.) The 2×2 matrices with determinant one, denoted SL(2, C), play a key role, as there is a map from SL(2,C) onto L+, that is 2-to-1 and a homomorphism. In this correspondence,...

We reexamine a scenario in which photons and gravitons arise as Goldstone bosons associated with the spontaneous breaking of Lorentz invariance. We study the emergence of Lorentz invariant low energy physics in an effective field theory framework, with non-Lorentz invariant effects arising from radiative corrections and higher order interactions. Spontaneous breaking of the Lorentz group also l...

In Lorentz-violating electrodynamics a steady current (and similarly a static charge) generates both static magnetic and electric fields. These induced fields, acting on interfering particles, change the interference pattern. We find that particle interference experiments are sensitive to small Lorentz violating effects, and thus they can be used to improve current bounds on some Lorentz-violat...

The relationship between Albert Einstein’s special theory of relativity and Hendrik A. Lorentz’s ether theory is best understood in terms of competing interpretations of Lorentz invariance. In the 1890s, Lorentz proved and exploited the Lorentz invariance of Maxwell’s equations, the laws governing electromagnetic fields in the ether, with what he called the theorem of corresponding states. To a...

In this paper we study translation surfaces with the non-degenerate third fundamental form in Lorentz- Minkowski space $mathbb{L}^{3}$. As a result, we classify translation surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form $III$ on the surface.

If Lorentz violation exists, it will affect the thresholds for pair creation processes. Lorentz-violating operators that change the maximum velocities of charged particles may increase or decrease the extinction rate of γ-rays moving through space. If the emissions from high-energy astrophysical sources do not show any signs of anomalous absorption, this allows us to place bounds on the Lorentz...

The Standard Model Extension (SME) provides the most general observer-independent field theoretical framework for investigations of Lorentz violation. The SME lagrangian by definition contains all Lorentz-violating interaction terms that can be written as observer scalars and that involve particle fields in the Standard Model and gravitational fields in a generalized theory of gravity. This inc...

the decomposition $gamma=bh$ of a group $gamma$ into a subset $b$ and a subgroup $h$ of $gamma$ induces, under general conditions, a group-like structure for $b$, known as a gyrogroup. the famous concrete realization of a gyrogroup, which motivated the emergence of gyrogroups into the mainstream, is the space of all relativistically admissible velocities along with a binary operation given by t...