Eugene Paul Wigner: Poincaré Group after Einstein

In 1905, Einstein formulated his special relativity for point particles. What happens if the particle has intrinsic space-time structure. For instance, Isaac Newton formulated his universal gravity law for two point particles. It took him twenty years to invent a new mathematics to take care of extended particles like the sun and earth.

Poincaré Group for Extended Particles

Lorentz Group for Optics

Click here for the two-by-two representation of the Lorentz group and its applications.

The photo of the Poincaré sphere on this webpage came from Christian Brosseau's book entitled "Fundamentals of Polarized Light, A Statistical Optics Approach" (Wiley, New York, 1998). I am grateful to Professor Brosseau for sending me a copy of this book.