Masters theses : Statistics

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THE SPINOR BUNDLE AND ITS APPLICATION
(2014) AHMED ALI MOHAMED MUSA
In this thesis we consider one of the most important mathematical and geometrical entity that generalizes the concept of tensor. This entity is the spinor field defined on a manifold. We discussed the forms of spinors in Euclidean space, R3, Rn, the space 𝐸2𝑣+1, andMinkowski space. The last space is the space describing space theory of relativity. We in fact constructed spinor field in this space and word it in the last chapter to formulate all fields. We also discussed the Dirac equation, which is widely known to be consistent with both the principles of quantum mechanics and the theory of special relativity. It is the first theory to account fully for special relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way. The equation also implied the existence of a new form of matter, antimatter, and actually predated its experimental discovery. It also provided a theoretical justification for the introduction of several-component wave functions in Pauli's phenomenological theory of spin.