English

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.

Keywords

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

R2 v1 2026-06-22T00:10:48.733Z