Complex extension of Wigner's theorem
Mathematical Physics
2013-09-13 v1 High Energy Physics - Theory
Differential Geometry
math.MP
Abstract
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.
Cite
@article{arxiv.1305.0658,
title = {Complex extension of Wigner's theorem},
author = {Dorje C. Brody},
journal= {arXiv preprint arXiv:1305.0658},
year = {2013}
}
Comments
13 pages, no figure