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In 1921 Weyl studied the invariance properties of quantum mechanics. In particular, he noted that the absolute phase of the wave function is not observable. In a formal and generic way, we consider a global transformation of the phase of a Dirac spinor. This can be expressed with the following unitary global gauge transformation 𝑈(𝛼)
Quantum field theory is complex. Ask ourselves why we bother with all these quantum fields in the first place? QED is a field theory of well-defined perturbation expansion and in principle any physical prediction can be calculated with practically infinite precision. So, in this chapter we explore the techniques associated with computing “higher-order” or “purely quantum” effects of electromagnetism. The 𝑆-matrix was written as the Dyson expansion (see Section 9.2), where the factor in the expansion is the electric elementary charge 𝑒.
In contradistinction to quantum electrodynamics, the Fermi theory is not renormalizable. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged vector particle exchange (the so-called 𝑊+ and 𝑊− bosons): theories with massive charged vector bosons are not renormalizable either.
The first speculations about “charm” were made in the mid-1960s [230], and full attention to it was given in the 1970s with the advent of the Cabibbo–GIM mechanism, as discussed in Section 23.13. In 1970 Drell and Yan discussed the production of massive lepton pairs in hadron–hadron collisions.