Abstract

Canonical transforms are a powerful tool in analyzing linear phenomena in science, engineering, and mathematics. Since special relativity is a linear transformation, it follows that it can be analyzed in terms of canonical transform. We recently proved that three dimensions suffice to analyze all canonical transformations. Using the well-known fact that canonical transforms associate integrals with matrices, we write down, to the best of our knowledge for the first time, the specific integrals representing rotations, boosts, and the Wigner rotation. It immediately follows that we have demonstrated the basic properties of the Lorentz group in terms of ideal cylindrical lenses in the paraxial approximation. Extending these results to the Poincare group corresponds to misaligning the lenses along the optical axis.

© 1989 Optical Society of America