Mathematical Derivation of Angular Momenta in Quantum Physics

• 作者: Daniel Grucker
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: Quantum Systems SPIN 1/2 SPIN 1 Particle Physics SPACETIME ALGEBRA
• 年，卷（期）: 2013,（7）
• 页码范围: 930-939
• 页数: 10页
• 分类号: O1

摘要

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.