The Clifford algebra of differential forms
type: Item
instance of: scholarly article
title: The Clifford algebra of differential forms
zbMATH Open document ID: 0572.15011
DOI: 10.1007/BF00052466
author: G. P. Wene
author: Nikos A. Salingaros
published in: Acta Applicandae Mathematicae
publication date: 1985-01-01T00:00:00Z
review text: Clifford algebras are discussed in the realization of differential forms in Minkowski space-time. Explicit solutions of the Klein-Gordon equation and the Kähler-Dirac equation in this realization are constructed. An important result is that a massive spin-1/2 particle cannot be mathematically accommodated in real Minkowski space with metric \((-1,-1,- 1,+1)\); such a particle can be accommodated either in the Majorana representation of the Dirac algebra with metric \((+1,+1,+1,-1)\) or in a complex Clifford algebra.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 15A90
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 58A10
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 3912547
zbMATH Keywords: spinors
zbMATH Keywords: differential forms
zbMATH Keywords: Kähler-Dirac equation
zbMATH Keywords: Klein-Gordon equation
MaRDI profile type: Publication
cites work: Q5525829
cites work: Spinors in n Dimensions
cites work: Q5830680
cites work: Q5824567
cites work: Q5574699
cites work: Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
cites work: Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis
cites work: Two-dimensional Ising correlations: The SMJ analysis
cites work: Q3287742
cites work: Electromagnetism and the holomorphic properties of spacetime
cites work: An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation
cites work: Generalized quaternions and spacetime symmetries
cites work: Some remarks on the tensorial linearization of general and linearly separable boolean functions
cites work: Exceptional gauge groups and quantum theory
cites work: Q5334539
cites work: Der innere Differentialkalkül
cites work: Q3853779
cites work: Realization, extension, and classification of certain physically important groups and algebras
cites work: Physical algebras in four dimensions. I: The Clifford algebra in Minkowski spacetime
cites work: Geometry of the Dirac theory
cites work: Space-time algebra approach to curvature
cites work: Fermions without spinors
cites work: Clifford modules
cites work: Q3890822
cites work: The Sequential Design of Experiments for Infinitely Many States of Nature
cites work: Algebras with three anticommuting elements. I. Spinors and quaternions
cites work: Algebras with three anticommuting elements. II. Two algebras over a singular field
cites work: A generalization of the construction of Ilamed and Salingaros
cites work: On the classification of Clifford algebras and their relation to spinors in n dimensions
cites work: The relationship between finite groups and Clifford algebras
cites work: Q5634146
cites work: Generalization of the Cauchy-Riemann Equations and Representations of the Rotation Group
cites work: Multivector functions
cites work: On the singularities of functions with values in a Clifford algebra
cites work: Spinor valued regular functions
cites work: Axially symmetric vector fields and their complex potentials
cites work: Complexified clifford analysis
cites work: Clifford analysis with generalized elliptic and quasi elliptic functions
cites work: Singularities and laurent expansions in complex clifford analysis
cites work: Eight-dimensional spinor representation of the Poincaré group
cites work: Clifford algebra approach to twistors
cites work: On the relationship between twistors and Clifford algebras
cites work: On geometrical properties of spinor structure
cites work: The theory of spinors via involutions and its application to the representations of the Lorentz group
cites work: Covariant objects and invariant equations on fiber bundles
cites work: Quaternionic analysis
cites work: Division algebras, (pseudo)orthogonal groups and spinors
cites work: Q5513537
cites work: Algebraic topology and elliptic operators
cites work: BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS
cites work: The index of elliptic operators. I
cites work: The index of elliptic operators. III
cites work: The index of elliptic operators. IV, V
cites work: On the heat equation and the index theorem
cites work: Curvature and the eigenvalues of the Laplacian for elliptic complexes
cites work: Q4098405
cites work: Topics in K-theory. L. Hodgkin: The equivariant Künneth theorem in K- theory. V. Snaith: Dyer-Lashof operations in K-theory
cites work: Algebraic K-theory. Proceedings of the conference, held at Northwestern University, Evanston, January 12-16, 1976

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cites work: Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory

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cites work: Translation-invariant integrals, and Fourier analysis on Clifford and Grassmann algebras

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cites work: Automorphisms of the canonical anticommutation relations and index theory

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cites work: Absence of vacuum polarisation in Fock space

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cites work: Automorphisms of the infinite dimensional Clifford algebra and the Atiyah-Singer mod 2 index

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cites work: Infinite dimensional groups and quantum field theory

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cites work: Differential forms. With applications to the physical sciences

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cites work: Q5615555

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cites work: Relativistic motion of a charged particle, the Lorentz group, and the Thomas precession

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cites work: Linear Representation of Spinors by Tensors

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cites work: Physical algebras in four dimensions. II: The Majorana algebra

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cites work: Q5576969

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cites work: Quantum field theory techniques in graphical enumeration

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cites work: Relativistic scalar products of γ matrices

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cites work: Q5834694

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cites work: Q5569204

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cites work: Q3236717