GEOMETRIC CALCULUS AND ELEMENTARY PARTICLES
GEOMETRIC CALCULUS AND ELEMENTARY PARTICLES S>Using Clifford algebra, a coordinate-free geometric calculus for non- Euclidean metric manifolds is developed, in which vectors and spinors appear on equal footing. A simple generalized covariant derivative is introduced, which applies to both vectors and spinors. Gravitational interactions arise from requiring covariance of the derivative under a local gauge group of Lorentz transformatnons. The Clifford algebra D/sub 4/ of space-time is examined in detail, and a geometric basis for isospace is found. Fermions are represented by ideals of D/sub 4/. Complex numbers arise naturally, and it follows that a geometric interpretation can be given to antiparticle conjugation. Several invariant kinds of conjugation'' in D/sub 4/ are found, and their possible physical interpretations are examined in terms of specific models for physical interactions. A model of weak interactions mediated by bosons is examined, in which the asymmetry parameters of hyperon decay are related to a cancellation of amplitudes that change the strangeness of a system by 2. (Dissertation Abstr.)
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