ABSTRACT
This chapter is devoted to the discussion of the ultraviolet divergences encountered in the calculation of Feynman diagrams involving loops in quantum field theory. After a short introduction to the method of dimensional regularisation, the treatment of divergences, leading to the replacement of the bare quantities appearing in the Lagrangian with the corresponding measured quantities, is ana- lysed considering the case of QED. The explicit expressions of the renormalised interaction vertex, photon and electron propagators - obtained including corrections of second order in the fine structure constant https://www.w3.org/1998/Math/MathML" display="inline"> α = e 2 / 4 π associated with one-loop diagrams - are derived in detail, and the corresponding renormalisation constants, are defined. The fundamental Ward's identity discussed in Chapter 4 is employed to demonstrate that the renormalisation of the https://www.w3.org/1998/Math/MathML" display="inline"> Z 1 , Z 2 and Z 3 electron charge arising from the corrections to the vertex and to the electron propagator exactly compensate one another, as required by the universality of electric charge.
