Charged-particle mechanics in Lie-Poisson electrodynamics is formulated with explicit gauge-invariant coordinates and action, and exact solutions are worked out for the λ-Minkowski and other cases.
Symmetry, Gravity and Noncommutativity
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We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical noncommutative gauge transformations is analysed in detail and it is shown how noncommutative Yang-Mills theory can be related to a gravity theory. The construction of twisted spacetime symmetries and their role in constructing a noncommutative extension of general relativity is described. We also analyse certain generic features of noncommutative gauge theories on D-branes in curved spaces, treating several explicit examples of superstring backgrounds.
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Charged Particle in Lie-Poisson Electrodynamics
Charged-particle mechanics in Lie-Poisson electrodynamics is formulated with explicit gauge-invariant coordinates and action, and exact solutions are worked out for the λ-Minkowski and other cases.