## 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(2*j*+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*,
*γ*_{μ},
*σ*_{μν},
*γ*_{5}γ_{μ}, and
*γ*_{5}, 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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