Operator algebras associated to the Klein-Gordon position
representation
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.