Parametrizing Clifford Algebras' Matrix Generators with Euler Angles
Abstract
A parametrization, given by the Euler angles, of Hermitian matrix generators of even and odd-degenerate Clifford algebras is constructed by means of the Kronecker product of a parametrized version of Pauli matrices and by the identification of all possible anticommutation sets for a given algebra. The internal parametrization of the matrix generators allows a straightforward interpretation in terms of rotations, and in the absence of a similarity transformation can be reduced to the canonical representations by an appropriate choice of parameters. The parametric matrix generators of 2nd and 4th-order are linearly decomposed in terms of Pauli, Dirac, and 4th-order Gell-Mann matrices establishing a direct correspondence between the bases. In addition, and with the expectation for further applications in group theory, a linear decomposition of GL(4) matrices on the basis of the parametric 4th-order matrix generators and in terms of four-vector parameters is explored. By establishing unitary conditions, a parametrization of two sub-groups of SU(4) is achieved.
Cite
@article{arxiv.2310.03962,
title = {Parametrizing Clifford Algebras' Matrix Generators with Euler Angles},
author = {Manuel Beato Vásquez and Melvin Arias Polanco},
journal= {arXiv preprint arXiv:2310.03962},
year = {2023}
}