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Eight-dimensional spinor representation of the Poincaré group

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Abstract

Finite-dimensional matrix representations of the Poincaré group are discussed with particular emphasis on the eight-dimensional spinor representation. It is speculated that the complex eight-dimensional representation space might be interpreted as a more fundamental entity than Minkowski space, being in a sense a square root of the latter. One can model the usual position, momentum, and angular momentum variables of a particle of nonzero rest mass and arbitrary spin by real bilinear forms in the 8-spinor components, and obtain their correct equations of motion by subjecting the spinor to a Schrödinger-like evolution equation.

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Authors and Affiliations

  1. School of Physics, University of Sydney, 2006, Sydney, NSW, Australia

    G. H. Derrick

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  1. G. H. Derrick
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Derrick, G.H. Eight-dimensional spinor representation of the Poincaré group. Int J Theor Phys 23, 359–393 (1984). https://doi.org/10.1007/BF02114515

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