Operator algebras associated with the Klein-Gordon position representation in relativistic quantum mechanics

Details Operator algebras associated with the Klein-Gordon position representation in relativistic quantum mechanics Operator algebras associated with the Klein-Gordon position representation in relativistic quantum mechanics

2002-09-07

arxiv.org/abs/math/0209079v1

Mathematics

Operator Algebras

28 pages

Scientific paper

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.

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