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Internal Space-time Symmetries of Particles derivable from Periodic Systems in Optics

While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into three conjugate classes depending on their traces, optical systems force us to establish continuity from one class to another. It is noted that those three classes are equivalent to three different branches of Wigner's little groups dictating the internal space-time symmetries massive, massless, and imaginary-mass particles. It is shown that the periodic systems in optics can also be described by have the same class-based matrix algebra. The optical system allow us to make continuous, but not analytic, transitions from massiv to massless, and massless to imaginary-mass cases.