Clifford algebra \(C\ell _{3}(\mathbb C)\) for applications to field theories

DOI10.1007/s10773-011-0822-yzbMath1236.81156OpenAlexW2165223208MaRDI QIDQ763465

Benoit Panicaud

Publication date: 9 March 2012

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-011-0822-y

zbMATH Keywords

general relativityClifford algebraelectromagnetismbiquaternionsfield theoriesLense-Thirring effectMaxwell-Proca equationsmultivectorial analysis

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Yang-Mills and other gauge theories in quantum field theory (81T13) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Clifford algebras, spinors (15A66) Electromagnetic theory (general) (78A25)

Related Items (6)

A Clifford algebra approach to the classical problem of a charge in a magnetic monopole field ⋮ Application of Clifford algebra \(C\ell_3(\mathbb C)\) to continuum and engineering mechanics ⋮ The complex algebra of physical space: a framework for relativity ⋮ Phenomenology from Dirac equation with Euclidean-Minkowskian ``gravity phase ⋮ Higher spin quaternion waves in the Klein-Gordon theory ⋮ On the use of Clifford algebra \(C\ell_3(\mathbb{C})\) with continuous media, for applications to multiphysical circuits

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Poincaré mass operator in terms of a hyperbolic algebra
• Symmetries in the hyperbolic Hilbert space
• Relativistic quantum physics with hyperbolic numbers
• Spinors in the hyperbolic algebra
• Gravitoelectromagnetism in a complex Clifford algebra
• Dirac equation on hyperbolic octonions
• Canonical bases for real representations of Clifford algebras
• The spacetime algebra approach to massive classical electrodynamics with magnetic monopoles
• Extended Grassmann and Clifford algebras
• Neural networks in multidimensional domains. Fundamentals and new trends in modelling and control
• Canonical planetary perturbation equations for velocity-dependent forces, and the Lense-Thirring precession
• Comment: Quaternionic, complex, duplex and real Clifford algebras
• The Lense-Thirring effect and Mach's principle
• Self-dual codes and invariant theory
• Signature of gravity in conic sedenions
• Gravity and electromagnetism on conic sedenions
• Hypernumbers and relativity
• The many faces of Maxwell, Dirac and Einstein equations. A Clifford bundle approach

This page was built for publication: Clifford algebra \(C\ell _{3}(\mathbb C)\) for applications to field theories