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Wigner’s Space-Time Symmetries Based on the Two-by-Two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2). It is shown that this oscillator system contains the essential features of Wigner’s little groups dictating the internal space-time symmetries of particles in the …