Transformations on the set of all n-dimensional subspaces of a Hilbert space preserving principal angles
Functional Analysis
2009-10-31 v1 Mathematical Physics
math.MP
Operator Algebras
Abstract
Wigner's classical theorem on symmetry transformations plays a fundamental role in quantum mechanics. It can be formulated, for example, in the following way: Every bijective transformation on the set L of all 1-dimensional subspaces of a Hilbert space H which preserves the angle between the elements of L is induced by either a unitary or an antiunitary operator on H. The aim of this paper is to extend Wigner's result from the 1-dimensional case to the case of n-dimensional subspaces of H with n fixed.
Keywords
Cite
@article{arxiv.math/0011029,
title = {Transformations on the set of all n-dimensional subspaces of a Hilbert space preserving principal angles},
author = {Lajos Molnar},
journal= {arXiv preprint arXiv:math/0011029},
year = {2009}
}
Comments
20 pages. To appear in Commun. Math. Phys