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E. before M → ∞. g. Quantum Gravity does not destroy Coulombs Law! Demanding this of our theory is equivalent to saying that we want our theory to be renormalisable. 5. 2). 2) m2 where c0 , c1 and d1 are constants, determined by the calculation. In order to evaluate Mf i numerically, however, we must express it in terms of the known parameter eˆ. 1 Diagrams for vertex renormalisation in qed up to one loop. 2 Some diagrams for electron–electron scattering in qed up to one loop. where the ellipsis denotes terms of order eˆ6 and above.

The C term gives the splitting between the 2s 1/2 and 2p1/2 levels of the hydrogen atom, known as the Lamb shift. Bethe’s calculation [3] of the Lamb shift, done during a train ride to Schenectady in June 1947, was an early triumph for quantum field theory. Here too, the current agreement between theory and experiment is impressive. 41). When a theory is renormalisable, all divergences can be removed in this way. Thus, for qed, if the original Lagrangian is (ignoring the gaugefixing term), 1 L = − Fµν F µν + iψ ∂/ψ − eψ Aψ / − mψψ, 4 then redefine everything by: 1/2 ψ = Z2 ψR , Z1 eˆ, e = Ze eˆ = 1/2 Z2 Z3 1/2 Aµ = Z3 AµR , m = Zm m, ˆ where the subscript R stands for “renormalised”.

A second 2π rotation gets you back to where you started.

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