2020 Impact factor 4.590
Particles and Fields
Eur. Phys. J. C 17, 359-366
DOI 10.1007/s100520000470

Leibniz rules and reality conditions

G. Fiore1 - J. Madore2,3

1 Dip. di Matematica e Applicazioni, Fac. di Ingegneria, Università di Napoli, V. Claudio 21, 80125 Napoli, Italy
2 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München, Germany
3 Laboratoire de Physique Théorique et Hautes Energies, Université de Paris-Sud, Bâtiment 211, 91405 Orsay, France

Received: 6 June 2000 / Published online: 9 August 2000 - © Springer-Verlag 2000

An analysis is made of reality conditions within the context of non-commutative geometry. We show that if a covariant derivative satisfies a given left Leibniz rule then a right Leibniz rule fixes the reality condition for the covariant derivative itself. We show also that the map which determines the right Leibniz rule must satisfy the braid equation if the extension of the covariant derivative to tensor products is to satisfy the reality condition.

Copyright Società Italiana di Fisica, Springer-Verlag 2000