Operator algebras associated with the Klein-Gordon position representation in relativistic quantum mechanics
Operator Algebras
2007-05-23 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
We initiate a mathematically rigorous study of Klein-Gordon position operators in single-particle relativistic quantum mechanics. Although not self-adjoint, these operators have real spectrum and enjoy a limited form of spectral decomposition. The associated C*-algebras are identifiable as crossed products. We also introduce a variety of non self-adjoint operator algebras associated with the Klein-Gordon position representation; these algebras are commutative and continuously (but not homeomorphically) embeddable in corresponding function algebras. Several open problems are indicated.
Keywords
Cite
@article{arxiv.math/0209079,
title = {Operator algebras associated with the Klein-Gordon position representation in relativistic quantum mechanics},
author = {Nik Weaver},
journal= {arXiv preprint arXiv:math/0209079},
year = {2007}
}
Comments
28 pages