By Forshaw J.
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Additional info for An introduction to QED and QCD
47) tr(γ µ1 · · · γ µn ) = 0 for n odd. 47). 21), we find 2e4 1 |Mf i|2 = 2 s2 + u2 − 4(m2e + m2µ )(s + u) + 6(m2e + m2µ )2 . 49) dΩ∗ 32π 2 s t2 for the differential cross section in the centre of mass frame. 49). 2 Lowest order Feynman diagrams for electron–electron scattering. Other calculations of cross sections or decay rates will follow the same steps we have used above. You draw the diagrams, write down the amplitude, square it and evaluate the traces (if you are using spin sum/averages).
Some strong interaction corrections to this part of the process can be calculated perturbatively. As the quark heads off out of the proton, however, the low energy strong interactions cut in again and “hadronise” the quark into the particles you actually detect. 5. We now try to repeat the procedure we used for renormalising the coupling in qed, but this time in qcd, which is also a renormalisable theory. 6. Looking at the second of these new diagrams, it is ultraviolet divergent (containing a ln M 2 term) and is also infrared divergent, since there is no mass to regulate the low momentum modes.
A particularly important covector is obtained by letting ∂/∂x µ act on a scalar φ: ∂φ ≡ ∂µ φ ∂xµ Show that ∂µ does transform like xµ and not xµ . Electromagnetism The four Maxwell equations are: ∇·E = ρ ǫ0 ∇×E =− ∇·B=0 ∂B ∂t ∇ × B = µ0 J + µ0 ǫ0 ∂E ∂t Which physical laws are represented by each of these equations? Show that ∂ρ +∇·J=0 ∂t and explain the significance of this equation. Verify that it can be written in manifestly covariant form ∂µ J µ = 0 where J µ = (cρ, J). Introduce scalar and vector potentials φ and A by defining B = ∇ × A and E = −∇φ − ∂A/∂t, and recall the gauge invariance of electrodynamics which says that E and B are unchanged when A → A + ∇Λ and φ → φ − ∂Λ ∂t for any scalar function Λ.