Electromagnetic interactions

The electromagnetic interaction is described by a gauge theory headed by the symmetry group U(1)_{EM} whose density of the Lagrangian can be written as:

 \mathcal{L} = i\overline{\psi}(x)\gamma^\mu \mathcal{D}_\mu\psi(x) - m\overline{\psi}(x)\psi(x) -\frac{1}{4}F_{\mu \nu}F^{\mu \nu}

where F_{\mu \nu}=\partial_\mu A_\nu - \partial_\nu A_\mu is the electromagnetic field tensor and \mathcal{D}_\mu=\partial_\mu + ieA_\mu + ieB_\mu is the gauge covariant derivative, with A_\mu indicating the covariant four-potential of the electromagnetic field, generated by the charge e; B_\mu is the external field due to an eventual external source; e is the coupling constant that coincides with the electric charge of the bispinor field.

Things get more interesting when one considers the electroweak unification..


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