Complex extension of Wigner’s theorem

Dorje C. Brody

Wigner’s theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed, we obtain the following complex generalisation of Wigner’s theorem: a holomorphically projective (complex geodesic-curves preserving) transformation on a quantum state space must be generated by a Hamiltonian that is not necessarily Hermitian.

http://arxiv.org/abs/1305.0658
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Differential Geometry (math.DG)

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