Abstract
The classical Kähler equation for an inhomogeneous differential form is analysed in some detail with respect to the physical properties of its Minkowski space solutions. Although the components of the field contain only integer representations of the Lorentz group for a physical interpretation of the quantum theory, we impose fermionic commutators. The electromagnetic interactions are identical to those of a Dirac spinor field with an extra fourfold degeneracy. Possibilities for the interpretation of the extra degrees of freedom are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kähler, E.: Der innere Differentialkalkül. Rend. Mat. (3–4)21, 425 (1962)
Darwin, C.G.: The wave equations of the electron. Proc. R. Soc.118, 654 (1928)
Graf, W.: Differential forms as spinors. Ann. Inst. Henri PoincaréXXIX, 85 (1978)
See for example, Hitchin, N.: Harmonic spinors. Adv. Math.14, 1 (1974)
Benn, I.M., Tucker, R.W.: Gauge field interactions from extra dimensional gravity. Phys. Lett.112B, 344 (1982)
Benn, I.M., Tucker, R.W.: A Riemannian description of non-abelian gauge interactions. Lancaster preprint (1982)
Author information
Authors and Affiliations
Additional information
Communicated by S. W. Hawking
Rights and permissions
About this article
Cite this article
Benn, I.M., Tucker, R.W. Fermions without spinors. Commun.Math. Phys. 89, 341–362 (1983). https://doi.org/10.1007/BF01214659
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01214659