Eur. Phys. J. C 18, 785-794
DOI: 10.1007/s100520100566

External fields as intrinsic geometry

J. Madore^{1, 2}, S. Schraml^{2, 3}, P. Schupp³ and J. Wess<sup>2, 3

1</sup>  Laboratoire de Physique Théorique, Université de Paris-Sud, Bâtiment 211, 91405 Orsay, France
²  Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München, Germany
³  Sektion Physik, Ludwig-Maximilian Universität, Theresienstrasse 37, 80333 München, Germany

(Received: 1 December 2000 / Published online: 23 January 2001 -© Springer-Verlag 2001)

Abstract
There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external fields which can be absorbed into an appropriate redefinition of the geometry, this time a noncommutative one. We shall also recall some previous incidences of the same phenomena involving bosonic field theories. It is known that some such theories on the commutative geometry of space-time can be re-expressed as abelian-gauge theory in an appropriate noncommutative geometry. The noncommutative structure can be considered as containing extra modes all of whose dynamics are given by the one abelian action.

© Società Italiana di Fisica, Springer-Verlag 2001