In addition, there are vacuum polarization diagrams in QCD which arise from gluon loops.For every vacuum polarization Feynman diagram in QED, there is a corresponding vacuum polarization in QCD.Short distance higher effective charge.Long distance low more dielectric (vacuum polarization) lower effective charge.The effective coupling strength depends on the effective dielectric constant of the vacuum:where is the effective dielectric constant.Even in QED, the coupling strength is NOT a coupling constant.QED lacks similar three-or four-photon vertices because the photon carries no electromagnetic charge.Because gluons carry color charge, there are three-gluon and four-gluon vertices as well as quark-quark-gluon vertices.Each gluon carries a color and an anti-color. Strong charge (whimsically called color) comes in three varieties, often called blue, red, and green.The coupling strength at each vertex depends on the momentum transfer (as is true in QED, but at a much reduced level).In place of photons, the quanta of the strong field are called gluons.The Feynman diagrams for strong interactions look very much like those for QED.Putting it Together M = + + + + + Physics 841 These matrix elements will be smaller than the first order QED matrix elements for the same process (same incident and final particles) because each vertex has a coupling strength.Just as we have second order perturbation theory in non-relativistic quantum mechanics, we have second order perturbation theory in quantum field theories.The third amplitude represents in the lowest order amplitude for Compton scattering in which a photon scatters from and electron producing a photon and an electron in the final state.The second amplitude is the exact inverse, two photon production of an electron positron pair. The first amplitude describes electron positron annihilation producing two photons.Essentially the same Feynman diagram describes the amplitudes for related processes, as indicated by these three examples.= M = + exchange annihilation Transition amplitudes (matrix elements) must be summed over indistinguishable initial and final states. Physics 841Īdding Amplitudes Note that an electron going backward in time is equivalent to an electron going forward in time. Note that the photon carries no electric charge this is a neutral current interaction. Bhabha scattering is the process electron plus positron goes to electron plus positron.The invariant masses of internal lines (like the photon here) are defined by conservation of energy and momentum, not the nature of the particle. Moller scattering is the basic first-order perturbative term in electron-electron scattering.Each vertex has a coupling strength characteristic of the interaction. Energy and momentum are conserved at each vertex. Note that in my convention, time flows to the right. The basic vertex shows the coupling of a charged particle (an electron here) to a quantum of the electromagnetic field, the photon.Our focus today will be on some of the concepts which unify and also which distinguish the quantum field theories of the strong, weak, and electromagnetic interactions.More specifically, Feynman diagrams correspond to calculations of transition amplitudes in perturbation theory.Feynman diagrams represent quantum mechanical transition amplitudes, M, that appear in the formulas for cross-sections and decay rates.All known interactions can be described in terms of forces forces:.Introduction to Feynman Diagramsand Dynamics of Interactions
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