"Poisson electrodynamics" | Colóquio do DFMA

Abstract: Gauge theories on noncommutative spaces with a position-dependent noncommutativity tensor $\Theta^{ab}(x)$ present a fundamental difficulty: ordinary derivatives do not satisfy the Leibniz rule with respect to the corresponding Poisson bracket. Consequently, the standard construction of gauge transformations, field strengths, and gauge-invariant actions must be deformed. In this talk, I will describe a geometric construction of Poisson electrodynamics, a semiclassical approximation to noncommutative gauge theory that is first order in $\hbar$ but exact to all orders in $\Theta$. Using symplectic realizations and groupoids, we construct infinitesimal and finite gauge transformations, covariant field strengths, gauge-invariant actions, and Maxwell–Poisson equations. I will also describe the consistent coupling to charged particles and show how curved momentum space can lead to a maximal kinetic energy and confinement even in a repulsive Coulomb potential.

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