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

2002/09/07 by Nik Weaver, Weaver, Nik
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.FA #math.MP #math.OA #msc:46J99 #msc:46L52 #msc:47L15 #msc:47L30 #msc:47L90 #msc:81R15

paper · pdf · doi:10.48550/arxiv.math/0209079

28 pages

arxiv created 2002/09/07 · arxiv updated 2009/11/30

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.

Related

• An Algebraic-Recursive Approach to Generate Higher-Order Symmetry Operators for Schrödinger and Klein-Gordon equations
• Algebra of symmetry operators for Klein-Gordon-Fock equation
• Localization of scalar quantum fields on Minkowski space-time
• Klein-Gordon equation within the real Hilbert space formalism
• Algebras and their Covariant representations in quantum gravity