Time parameterizations and spin supplementary conditions of the Mathisson-Papapetrou-Dixon equations

Understand

The implications of two different time constraints on the Mathisson-Papapetrou-Dixon (MPD) equations are discussed under three spin supplementary conditions (SSC).

• For this reason the MPD equations are revisited without specifying the affine parameter and several relations are reintroduced in their general form.
• The latter allows to investigate the consequences of combining the Mathisson-Pirani (MP) SSC, the Tulczyjew-Dixon (TD) SSC and the Ohashi-Kyrian-Semer\'{a}k (OKS) SSC with two affine parameter types: the proper time on one hand and the parameterizations introduced in [Gen.
• Rel.