A study of arbitrary sequences of planar rotations and conventional Lorentz transformations in two-dimensional space

Iyer, Chandru and Prabhu, G. M. (2007) A study of arbitrary sequences of planar rotations and conventional Lorentz transformations in two-dimensional space. Technical Report 07-03, Computer Science, Iowa State University.

Abstract

We develop a general form of Lorentz transformations in two-dimensional space. This takes two forms: (i) a conventional Lorentz followed by a spatial rotation and then by another conventional Lorentz (LRL), and (ii) a spatial rotation followed by a conventional Lorentz and then followed by another spatial rotation (RLR). It is shown that an LRL transformation can always be converted to a RLR transformation, but the converse is not always possible. Adopting a constructive approach without non-commutative complexities, our result leads to the conclusion that any arbitrary sequence of Rs and Ls can be reduced to a single RLR transformation. We also attach an Excel spreadsheet that automatically converts an LRL to RLR and vice versa (when possible).