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Mathematical Derivation of Angular Momenta in Quantum Physics

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DOI: 10.4236/jmp.2013.47125    6,595 Downloads   8,439 Views  
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

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