28 research outputs found
Aufbau und Funktion des On-line-Systems zur Datenverarbeitung und Experimentsteuerung bei SNEAK
Supersymmetry and Noncommutative Geometry
The purpose of this article is to apply the concept of the spectral triple,
the starting point for the analysis of noncommutative spaces in the sense of
A.~Connes, to the case where the algebra \cA contains both bosonic and
fermionic degrees of freedom. The operator \cD of the spectral triple under
consideration is the square root of the Dirac operator und thus the forms of
the generalized differential algebra constructed out of the spectral triple are
in a representation of the Lorentz group with integer spin if the form degree
is even and they are in a representation with half-integer spin if the form
degree is odd. However, we find that the 2-forms, obtained by squaring the
connection, contains exactly the components of the vector multiplet
representation of the supersymmetry algebra. This allows to construct an action
for supersymmetric Yang-Mills theory in the framework of noncommutative
geometry.Comment: 26pp., LaTe