Non-relativistic tachyons: a new representation of the Galilei group

TL;DR

This paper constructs a consistent non-relativistic limit of tachyonic representations of the Poincaré group, revealing novel properties of Galilean tachyons, such as evolution in space and nonlocalizability, enhancing understanding of tachyonic physics.

Contribution

It introduces a new nonstandard Galilei group representation derived from Poincaré contractions, providing a toy model for tachyonic behavior in non-relativistic physics.

Findings

Evolution occurs in spatial coordinates rather than time.

The modulus of three-momentum is invariant across Galilean observers.

Tachyonic objects are nonlocalizable in the standard sense.

Abstract

An algebraic characterization of the contractions of the Poincar\'e group permits a proper construction of a non-relativistic limit of its tachyonic representation. We arrive at a consistent, nonstandard representation of the Galilei group which was disregarded long ago by supposedly unphysical properties. The corresponding quantum (and classical) theory shares with the relativistic one their fundamentals, and serves as a toy model to better comprehend the unusual behavior of the tachyonic representation. For instance, we see that evolution takes place in a spatial coordinate rather than time, as for relativistic tachyons, but the modulus of the three-momentum is the same for all Galilean observers, leading to a new dispersion relation for a Galilean system. Furthermore, the tachyonic objects described by the new representation cannot be regarded as localizable in the standard sense.