**Mathematics**

Mathematically, QED is an abelian gauge theory with the symmetry group U(1). The gauge field, which mediates the interaction between the charged spin-1/2 fields, is the electromagnetic field. The QED Lagrangian for a spin-1/2 field interacting with the electromagnetic field is given by the real part of

where

- are Dirac matrices;
- a bispinor field of spin-1/2 particles (e.g. electron-positron field);
- , called "psi-bar", is sometimes referred to as Dirac adjoint;
- is the gauge covariant derivative;
*e*is the coupling constant, equal to the electric charge of the bispinor field;*A*_{μ}is the covariant four-potential of the electromagnetic field generated by the electron itself;*B*_{μ}is the external field imposed by external source;- is the electromagnetic field tensor.

Read more about this topic: Quantum Electrodynamics

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