Mathematical Derivation of Angular Momenta in Quantum Physics | Zendy

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Mathematical Derivation of Angular Momenta in Quantum Physics

Author(s) -

Daniel Grucker

Publication year - 2013

Publication title -

journal of modern physics

Language(s) - English

Resource type - Journals

eISSN - 2153-120X

pISSN - 2153-1196

DOI - 10.4236/jmp.2013.47125

Subject(s) - pauli matrices , physics , spins , clifford algebra , commutator , geometric algebra , spin (aerodynamics) , angular momentum , spacetime , pauli exclusion principle , lorentz transformation , quantum mechanics , rotation matrix , mathematical physics , classical mechanics , theoretical physics , lie algebra , algebra over a field , pure mathematics , mathematics , geometry , lie conformal algebra , thermodynamics , condensed matter physics

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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