Electromagnetic Theory with Quantum Principal Bundles

Abstract

The aim of this paper is to formulate a {\it non--commutative geometrical} version of the classical electromagnetic field theory in the vacuum with the Moyal--Weyl algebra as the space--time by using the theory of quantum principal bundles and quantum principal connections. As a result we will present the correct Maxwell equations in the vacuum of the model, in which we can appreciate the existence of electric and magnetic charges and currents. Finally, in the fourth section we are going to present a {\it mathematical model} for which there are instantons that are not solutions of the corresponding Yang--Mills equation.

References in corpus (13)

• A Gravity Theory on Noncommutative Spaces
• Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
• Strings in Background Electric Field, Space/Time Noncommutativity and A New Noncritical String Theory
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• Geometry of Quantum Principal Bundles I
• Twisted Gauge Theories
• Projective module description of the q-monopole
• Noncommutative spacetime symmetries: Twist versus covariance
• On the Space-Time Symmetries of Non-Commutative Gauge Theories
• Observables and Dispersion Relations in k-Minkowski Spacetime
• Noncommutative Induced Gauge Theories on Moyal Spaces
• On the energy-momentum tensor in Moyal space
• Topological Dyons