Abstract

The canonical-operator approach to Fourieroptics¹ has led to a new integral representation of special relativity that is different from either the Clifford algebra or spinor approach. An arbitrary Lorentz transformation can be decomposed into a rotation, a boost, and a translation. In my paper, the explicit forms of these parameters are derived, and some three-dimensional relativistic effects are discussed. In particular, it is shown that previous solutions of the Doppler effect have made unwarranted assumptions, have solved only an approximate equation, and/or have solved the problem implicitly instead of explicitly. The exact solution of the Doppler effect can be derived in a straightforward manner and generalizes the Wigner rotation to arbitrary velocities. It also provides a lower bound on the speed of the signal sent between source and receiver.

© 1990 Optical Society of America