zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The Dirac equation in exterior form. (English) Zbl 0587.58002
This paper is a continuation of the authors’ papers [ibid. 89, 341-362 (1983; Zbl 0527.58023); J. Phys. A 16, 4147-4153 (1983); Phys. Lett. B 130, 177-178 (1983)]. The authors, using the correspondence between the Clifford and exterior algebras, have written the Dirac equation in terms of differential forms. The covariances of the theory are examined. The authors have shown in detail the correspondence between an equation for a spinorial section of the Kähler-Atiyah bundle and the usual matrix formulation of the Dirac equation.
Reviewer: J.Kubarsky

58A10Differential forms (global analysis)
15A66Clifford algebras, spinors
81Q05Closed and approximate solutions to quantum-mechanical equations
Full Text: DOI
[1] K?hler, E.: Der innere Differentialkalk?l. Rend. Mat. (3-4)21, 425 (1962)
[2] Graf, W.: Differential forms as spinors. Ann. Inst. Henri Poincar?XXIX, 85 (1978)
[3] Benn, I.M., Tucker, R.W.: Fermions without spinors. Commun. Math. Phys.89, 341 (1983) · Zbl 0527.58023 · doi:10.1007/BF01214659
[4] Albert, A.A.: Structure of algebras. American Mathematical Society Colloquium Publications, Vol. XXIV, 1961 · Zbl 0109.12401
[5] Benn, I.M., Tucker, R.W.: Clifford analysis of exterior forms and Fermi-Bose symmetry. J. Phys. A16, 4147 (1983) · Zbl 0515.53022 · doi:10.1088/0305-4470/16/17/029
[6] Lounesto, P.: Scalar products of spinors and an extension of Brauer-Wall groups. Found. Phys.11, 721 (1981) · doi:10.1007/BF00726946
[7] Porteus, I.R.: Topological geometry. Cambridge: Cambridge University Press 1981
[8] Benn, I.M., Tucker, R.W.: A local right-spin covariant K?hler equation. Phys. Lett. B130, 177 (1983) · doi:10.1016/0370-2693(83)91037-7