2 research outputs found
On complexified mechanics and coquaternions
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.Comment: 11 pages, version to appear in Journal of Physics