Masters Thesis

U(1) x U(1) gauge theory applied to magnetic monopoles

In this paper we build up a U(1) (i.e. one dimensional unitary) gauge theory beginning with a standard complex scalar field Lagrangian, then by introducing a local gauge transformation and subsequently rede_ning the derivative, we will be able to obtain Maxwell's equations with the Noether current. This will show that electromagnetic fields arise in this form as the result of the invariance of the complex scalar field Lagrangian under local gauge transformations. From there we will extend to a U(1) _ U(1) theory by introducing a second vector potential which will result in Maxwell's equations allowing magnetic charge and a Lagrangian with an extra massless photon inconsistent with the Standard Model. Using the Higgs' mechanism this photon will gain mass and represent a new \magnetic photon." We will then extend the theory by introducing a second scalar potential which will result in conditions on magnetic and electric charge.

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