Mathematical Physics


A Poincare Conformal Matrix Lie Algebra

Authors: Richard Shurtleff

The Poincar\'{e} group of spacetime rotations and spacetime translations has been fundamental for over a century. Also a century old are efforts to find alternatives, efforts that include invoking the larger symmetry group of Maxwell's electrodynamics, the conformal group. In this paper an 8x8 matrix representation of the Poincare group is enhanced by defining a 4x4 matrix rep of the conformal group that acts on 4 of the 8 dimensions, a 4-spinor subset of 8-spinors. The matrix generators are described in detail and the commutation relations of the Lie algebra are displayed. There are additional generators needed to keep the enhanced algebra closed. The new generators add new transformations making a group larger than the direct product of the Poincare and conformal groups.

Comments: 11 page article plus 32 page Mathematica notebook in an Appendix = 43 pages. This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit

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[v1] 2018-11-23 06:42:56

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