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J. Frohlich, “Spin or Actually: Spin and Quantum Statistics p1-60 in The Spin, Poincaré Seminar 2007,” B. Duplantier, J. M. Raimond and V. Rivasseau, Eds., Birkhauser, Basel, 2009.

has been cited by the following article:

• TITLE: Mathematical Derivation of Angular Momenta in Quantum Physics

  AUTHORS: Daniel Grucker

  KEYWORDS: Quantum Systems; Spin 1/2; Spin 1; Particle Physics, Spacetime Algebra

  JOURNAL NAME: Journal of Modern Physics, Vol.4 No.7, July 8, 2013

  ABSTRACT: For a two-dimensional complex vector space, the spin matrices can be calculated directly from the angular momentum commutator definition. The 3 Pauli matrices are retrieved and 23 other triplet solutions are found. In the three-dimensional space, we show that no matrix fulfills the spin equations and preserves the norm of the vectors. By using a Clifford geometric algebra it is possible in the four-dimensional spacetime (STA) to retrieve the 24 different spins 1/2. In this framework, spins 1/2 are rotations characterized by multivectors composed of 3 vectors and 3 bivectors. Spins 1 can be defined as rotations characterized by 4 vectors, 6 bivectors and 4 trivectors which result in unit multivectors which preserve the norm. Let us note that this simple derivation retrieves the main spin properties of particle physics.