The Pauli algebra approach to special relativity

Abstract

The Pauli algebra P, in which the usual dot and cross products of 3-space vectors are combined in an associative, invertible, but non-commutative multiplication, provides a simple but powerful approach to problems in special relativity. Even though the Pauli algebra is the Clifford algebra for Euclidean 3-space, Minkowski 4-vectors and their products in the Minkowski metric appear in a natural and covariant way as elements of P. The authors review the algebra and develop a formulation which, although closely tied to elementary vector and functional analysis, nevertheless allows a compact coordinate-free treatment of essentially all problems in special relativity. They derive a number of useful results and show how the elements are related both to traditional Minkowski-space tensors and to elements of the Dirac algebra.