On complexified mechanics and coquaternions

Details On complexified mechanics and coquaternions On complexified mechanics and coquaternions

2010-12-03

arxiv.org/abs/1012.0757v2

J. Phys. A 44 (2011) 072001

Physics

Mathematical Physics

11 pages, version to appear in Journal of Physics A

Scientific paper

10.1088/1751-8113/44/7/072001

While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and coquaternionic (split-signature analogue of quaternions) extensions of Hamiltonian mechanics are introduced, and are shown to offer a unifying framework for complexified classical and quantum mechanics. In particular, quantum theories characterised by complex Hamiltonians invariant under space-time reflection are shown to be equivalent to certain coquaternionic extensions of Hermitian quantum theories. One of the interesting consequences is that the space-time dimension of these systems is six, not four, on account of the structures of coquaternionic quantum mechanics.

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