Quantum Electrodynamics - Mathematics

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.