The Poincaré mass operator in terms of a hyperbolic algebra

DOI10.1016/j.physletb.2005.03.011zbMath1247.81187arXivhep-th/0510198OpenAlexW2075763148MaRDI QIDQ451649

S. Ulrych

Publication date: 23 September 2012

Published in: Physics Letters. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/0510198

zbMATH Keywords

\(Cl(3,0)\) Clifford algebraPoincaré mass operator

Mathematics Subject Classification ID

Spinor and twistor methods applied to problems in quantum theory (81R25) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20)

Related Items (13)

\(f\)-algebra structure on hyperbolic numbers ⋮ Application of Clifford algebra \(C\ell_3(\mathbb C)\) to continuum and engineering mechanics ⋮ Von Neumann uniqueness theorem doesn't hold in hyperbolic quantum mechanics ⋮ FOURIER ANALYSIS OVER HYPERBOLIC ALGEBRA, PSEUDO-DIFFERENTIAL OPERATORS, AND HYPERBOLIC DEFORMATION OF CLASSICAL MECHANICS ⋮ On the consistency of the quantum-like representation algorithm for hyperbolic interference ⋮ Generalized Klein-Gordon field equations with octonion space-time (OST) algebra ⋮ Sedeonic equations in field theory ⋮ Scalar fields described by Dirac quaternion wave equation ⋮ Gauge invariance of sedeonic equations for massive and massless fields ⋮ Clifford algebra \(C\ell _{3}(\mathbb C)\) for applications to field theories ⋮ On the use of Clifford algebra \(C\ell_3(\mathbb{C})\) with continuous media, for applications to multiphysical circuits ⋮ Sedeonic equations of massive fields ⋮ Deformations of thermo-algebras and of Fock spaces on a ring, and open quantum systems

Cites Work

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• Hyperbolic Hilbert space
• Comment: Quaternionic, complex, duplex and real Clifford algebras
• Complex Clifford algebra and \(n\)th-order linear differential equations
• Unipodal algebra and 2nd-order linear differential equations
• Unipodal algebra and roots of polynomials: Report
• The Pauli algebra approach to special relativity
• Hyperbolic complex structures in physics
• The four-dimensional hyperbolic spherical harmonics

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