Abstract
In our preceding two papers we have developed synthetic differentialsupergeometry up to the basic theory of differential forms. In this paper we givethe notion of connection, as well as its accompanying notions of connection formand curvature form, superized in our synthetic context, and establish the secondBianchi identity synthetically.
Similar content being viewed by others
REFERENCES
Bartocci, C., Bruzzo, U., and Hernández-Ruipérez, D. (1991).The Geometry of Supermanifolds, Kluwer, Dordrecht. DeWitt, B. (1984).Supermanifolds, Cambridge University Press, Cambridge.
Kock, A. (1981).Synthetic Differential Geometry, Cambridge University Press, Cambridge.
Kock, A. (1996). Combinatorics of curvature and the Bianchi identity,Theory and Applications of Categories 2, 69-89.
Lavendhomme, R. (1996).Basic Concepts of Synthetic Differential Geometry, Kluwer, Dordrecht.
Manin, Y. I. (1988).Gauge Field Theory and Complex Geometry, Springer, Berlin and Heidelberg.
Moerdijk, I., and Reyes, G. E. (1991).Models for Smooth Infinitesimal Analysis, Springer-Verlag, New York.
Nishimura, H. (1998). Synthetic differential supergeometry,International Journal of Theoretical Physics,37, 2803-2822.
Nishimura, H. (1999). Differential forms in synthetic differential supergeometry,International Journal of Theoretical Physics,38, 653-663.
Nishimura, H. (2000). Another curvature in synthetic differential geometry,Bulletin Belgian Mathematical Society, to appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nishimura, H. Synthetic Theory of Superconnections. International Journal of Theoretical Physics 39, 297–320 (2000). https://doi.org/10.1023/A:1003632208750
Issue Date:
DOI: https://doi.org/10.1023/A:1003632208750