Special relativity with 2×2 matrices

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Abstract
The elegance and efficiency of a two-component spinor representation of the restricted Lorentz group is enhanced by expressing the 2×2 transformation matrices in exponential form. Various advantages suggest its use in undergraduate courses in place of the usual Minkowski-space formulation. One starts with 2×2 Hermitian matrices to represent real Lorentz four vectors. Matrix products quickly give other physical quantities, both of four-vector type and ’’six-vector’’ (complex three-vector) type, such as the complex electromagnetic field E+iB or a generalized angular momentum. All are easily transformed without explicit reference to Cartesian components by multiplication with 2×2 unimodular matrices. Numerous examples are presented.

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