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We consider a model that describes a charged particle in curved spacetime with external gauge fields by means of a recently proposed covariant phase-space formalism. In this formalism, which is more suited to find invariants, the phase-space brackets are changed to an extended algebra containing the field strength of the gauge fields. However the contribution from the electromagnetic interaction will alter the set of the Killing tensor equations in order to obtain some conserved quantities. With the Killing tensor still there is a geometric duality that implies in a completely non-trivial metric associated to the spacetime. Using this metric some geometrical invariants and currents are considered.

Geometrical invariants, conserved currents and new symmetries in a covariant phase-space dynamics