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Applications Of The Pauli Algebra And Other Geometric Algebras., Shazia. Hadi
Applications Of The Pauli Algebra And Other Geometric Algebras., Shazia. Hadi
Electronic Theses and Dissertations
Relationships among the complex numbers, quaternions, and the Pauli algebra are developed by presenting them as geometrical (Clifford) algebras. Rotations are examined using both quaternions and the Pauli algebra, and in particular, algorithms that are used in three-dimensional simulations and video games are formulated in the Pauli algebra. Relativity is presented using a number of formalisms, and the treatment of De Leo and Rotelli is clarified. The relationship between spinors and spacetime vectors is explored using the Pauli algebra. Dirac theory is exhibited using the Pauli algebra, and neutrino oscillations are discussed.Dept. of Physics. Paper copy at Leddy Library: Theses …
An Algebraic Basis For The Standard-Model Gauge Group., Gregory James. Trayling
An Algebraic Basis For The Standard-Model Gauge Group., Gregory James. Trayling
Electronic Theses and Dissertations
A geometric approach to the standard model in terms of the Clifford algebra Cℓ7 is advanced. The gauge symmetries and charge assignments of the fundamental fermions and the Higgs boson are seen to arise uniquely from a simple geometric model involving only four extra space-like dimensions. A key feature of the model is its use of double-sided operations on the algebraic spinors. Transformations separate naturally into left-sided or "exterior", and right-sided or "interior" types. The exterior transformations include those of the Poincare and SU(2) L groups, the interior ones include those of SU(3) C, and a unique double-sided form of …