ABSTRACT
This chapter gives a brief discussion of the specific features of the theory of massless vector (gauge) fields. The canonical quantization of the theory is nontrivial, because the corresponding Lagrangian is degenerate (or singular), i.e., for it there is no one–to-one relation between the velocities and momenta. The Ward–Slavnov identities are various differential relations describing the dependence of functional on the choice of gauge. They are obtained by means of a suitable change of integration variable B → B + δB. The electromagnetic field is the Yang–Mills field for the one-parameter Abelian group Γ. The renormalized S matrix on the fermionic mass shell is transverse and independent of the parameters n and c in the gauge condition.
