Mathematical Derivation of Angular Momenta in Quantum Physics
Daniel Grucker

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.

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D. Grucker, "Mathematical Derivation of Angular Momenta in Quantum Physics," Journal of Modern Physics, Vol. 4 No. 7, 2013, pp. 930-939. doi: 10.4236/jmp.2013.47125.

Conflicts of Interest

The authors declare no conflicts of interest.

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