Einstein's energy–momentum relation is applicable to particles of all speeds, including the particle at rest and the massless particle moving with the speed of light. If one formula or formalism is applicable to all speeds, we say it is "Lorentz-covariant." As for the internal space-time symmetries, there does not appear to be a clear way to approach this problem. For a particle at rest, there are three spin degrees of freedom. For a massless particle, there are helicity and gauge degrees of freedom. The aim of this book is to present one Lorentz-covariant picture of these two different space-time symmetries. Using the same mathematical tool, it is possible to give a Lorentz-covariant picture of Gell-Mann's quark model for the proton at rest and Feynman's parton model for the fast-moving proton. The mathematical formalism for these aspects of the Lorentz covariance is based on two-by-two matrices and harmonic oscillators which serve as two basic scientific languages for many different branches of physics. It is pointed out that the formalism presented in this book is applicable to various aspects of optical sciences of current interest.
Contents:- Introduction
- Einstein's Philosophical Base
- More about Einstein
- Einstein in the United States
- Introduction to the Lorentz Group
- Wigner's Little Groups
- Lorentz completion of the Little Groups
- Lorentz-covariant Harmonic Oscillators
- Quarks and Partons
- Feynman's Rest of the Universe
- Further Applications of the Lorentz Group
Readership: College students with basic knowledge in physics and mathematics.
Key Features:- Einstein's Lorentz covariance extended to internal space-time symmetries of elementary particles
- Concrete physical examples given to Wigner's subgroups of the Lorentz group
- Gell-Mann's quark model and Feynman's parton model as two limiting cases of one Lorentz-covariant entity, since Einstein's energy-momentum relations are applicable to both a massive particle at rest and a massless particle moving at the speed of light
