Grassmann-Cartan algebra and Klein-Gordon equations
type: Item
instance of: scholarly article
title: Grassmann-Cartan algebra and Klein-Gordon equations
zbMATH Open document ID: 0567.53018
DOI: 10.1007/BF02214073
author: J. F. Plebański
published in: International Journal of Theoretical Physics
publication date: 1984-01-01T00:00:00Z
review text: Let \(V=(M,g)\) be a Riemannian space over an n-dimensional differentiable manifold M with a non-singular metric g. At each point we have a graded Grassmann-Cartan algebra \(\Lambda =\oplus^{n}_{p=0}\Lambda^ p\) of differential forms and the usual differential mappings d and \(\delta\). The author studies the equations \((d+\delta +m)\alpha =0\), \(\alpha\in \Lambda\), and thus independently arrives at the so-called Dirac-Kähler equations, since there is no reference to many papers under this name. Then he reviews carefully and in detail the general geometrical notions, the properties of the above equation, special cases and some special explicit solutions.
Mathematics Subject Classification ID: 53B20
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 3905369
zbMATH Keywords: differential forms
zbMATH Keywords: Dirac-Kähler equations
reviewed by: A. O. Barut
MaRDI profile type: Publication
cites work: Q5824567
cites work: The vacuum in quantum electrodynamics
cites work: On The Characteristic Matrices of Covariant Systems
cites work: Principle of General Q Covariance
cites work: Differential forms. With applications to the physical sciences
cites work: The particle aspect of meson theory
cites work: Theory of filters
cites work: Scattering theory for the Klein-Gordon equation
Recommended article: Grassmannian Kaluza-Klein theory
Recommended article: Dirac and Klein–Gordon–Fock equations in Grumiller’s spacetime
Recommended article: Q3329862
Recommended article: Grassmann calculus, pseudoclassical mechanics, and geometric algebra
Recommended article: Grassmann coordinates and Lie algebras for unified models
Recommended article: Quantum field theory, Grassmannians, and algebraic curves
Recommended article: Deformation quantization, quantization and the Klein–Gordon equation
Recommended article: Algebraic approach to Kaluza-Klein models
Recommended article: Integrability of Klein–Gordon Equations
Recommended article: Algebra of symmetry operators and integration of the Klein-Gordon equation in an external electromagnetic field
description: scientific article; zbMATH DE number 3905369