Transformations on the set of all n-dimensional subspaces of a Hilbert space preserving principal angles

Details Transformations on the set of all n-dimensional subspaces of a Hilbert space preserving principal angles Transformations on the set of all n-dimensional subspaces of a Hilbert space preserving principal angles

2000-11-04

arxiv.org/abs/math/0011029v1

Mathematics

Functional Analysis

20 pages. To appear in Commun. Math. Phys

Scientific paper

10.1007/PL00005551

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.

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