The Dirac Algebra for Any Spin

David N. Williams

Institüt für Theoretische Physik
Eidgenössische Technische Hochschule
Zürich, 1964

Abstract: We study the generalization of the Dirac algebra to any spin in the 2(2j+1)-component formalism. We review the spinor calculus and the construction of generalized Pauli matrices for any spin, and a few properties of the wave equation and its solutions. We show how to compute and classify the analogs of the matrices in the Dirac algebra, I, γμ, σμν, γ5γμ, and γ5, and we derive the essential relations among them and their traces. These follow from the observation that the classification of matrices in the generalized Dirac algebra corresponds to a Clebsch-Gordan analysis within the structure resulting from discrete symmetry. We briefly mention the representation of scattering amplitudes.

Published in Lectures in Theoretical Physics, vol. VII A, Lorentz Group, (University of Colorado Press, Boulder, 1965), pp. 139–172.

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