Einstein''s energy–momentum relation is applicable to particles of all speed, including the particle at rest and the massless particle moving at 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 do 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 a mathematical tool for the Lorentz-covariant picture of this intrinsic space-time symmetry. 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. It is shown also that the same set of mathematical tools is applicable for understanding various aspects of optical sciences of current interest.
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