ABSTRACT
This Chapter describes the construction of the perturbative series for Quantum Electrodynamics, the theory of the interaction between electrons and photons. The treatment of QED can be extended trivially to the interactions of the other known charged leptons, https://www.w3.org/1998/Math/MathML" display="inline"> μ and τ particles. Hadronic, electrically charged particles like quarks do also interact with photons but the situation is complicated by the presence of dominant QCD interactions, see Chapters 20 and 21 for the overall picture. The QED Lagrangian is determined by two physical constants, the bare mass and electric charge of the electron: https://www.w3.org/1998/Math/MathML" display="inline"> m 0 and e 0 . The photon mass vanishes, due to the invariance of the theory under a commutative set of one-parameter gauge transformations on the electron and photon fields. Neither https://www.w3.org/1998/Math/MathML" display="inline"> m 0 nor e 0 are observable quantities. The renormalisation process, to be discussed in Chapter 11, consists of expressing the results of the theory in terms of the measurable charge and mass of the electron, https://www.w3.org/1998/Math/MathML" display="inline"> m and e . The construction of the perturbative series for the S-matrix, as an expansion in powers of https://www.w3.org/1998/Math/MathML" display="inline"> e 0 , which proceeds from the generating functional of the Green's functions, following the same steps illustrated for the scalar field. The construction of Feynman diagrams and the corresponding Feynman rules are illustrated in detail. The case of the two-point function to order https://www.w3.org/1998/Math/MathML" display="inline"> e 0 2 is discussed for illustration.
