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RESEARCH PRODUCT

Particles with Spin 1/2 and the Dirac Equation

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In order to identify the spin of a massive particle one must go to its rest system, perform rotations of the frame of reference, and study the transformation behaviour of one-particle states. This prescription was one of the essential results of Chap. 6. Furthermore, the spin \(1/2\) (electrons, protons, other fermions) is described by the fundamental representation of the group \(SU(2)\). The eigenstates of the observables \(\mathbf{{s}}^2\) and \(s_3\) transform by the \(D\)-matrix \(\mathbf{D }^{(1/2)}(\mathbf R )\) which is a two-valued function on \(\mathbb{R }^3\).