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Investigation of the force between two non-commutative U(2) monopoles Chu, Karene Ka Yin


The force between two widely separated 't Hooft-Polyakov monopoles involves an ordinary Coulomb force as well as an attractive force with the same magnitude mediated by a scalar field. Manton arrived at this fact using an ansatz he discovered for a weakly accelerating monopole [1]. We study Manton's method, eliminate its ambiguities, interpret the ansatz as the external force law for a monopole, and compare it with another approach that uses the stress-energy tensor [2]. We find that the force between two monopoles in non-commutative spacetime does not alter from that in commutative spacetime to first order in the non-commutative parameter, θ, both by extending Manton's method and by finding the total energy of the system. We investigate Manton's method at O(θ²) but find it not very promising . We understand that the non-commutativity starts to affect dynamics only at O(θ²).

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