Feynman amplitude

To complete the one-photon story, consider the exchange of a photon when "1" has spin-0 and "2" has spin-1/2. The Feynman amplitude is then given by... 

In Fig. 11, we give an overview of the fit of phase shifts by some modern meson-theoretic potentials. The solid line represents the prediction by the Bonn full model [15] while the dashed line is the Paris [14] prediction. The Bonn full model is an energy-dependent potential. This energy-dependence is inconvenient in nuclear structure applications. Therefore, a representation of the model in terms of relativistic, energy-independent Feynman amplitudes has been developed, using the relativistic, three-dimensional Blankenbecler-Sugar method [30]. This representation has become known as the Bonn B potential [6] . The dotted line in Fig. 11 shows the phase-shift... 

The virtual transitions between K° = sd and K° = sd that are responsible for the mass difference are given by the diagrams in Fig. 9.1. (The precise relation between the mass difference and the Feynman amplitude is derived in Sections 19.2 and 19.3.) The Feynman amplitudes... 

To get an estimate for the leptonic decay rates, note that vector boson effects are unimportant, so that from Section 1.2 the Feynman amplitude for the pseudo-scalar P —> decay will be given by (0 means vacuum)... 

Using the rules given in Appendix 2 the Feynman amplitude can be written down and has the form... 

We give here, without derivation, the rules for calculating (up to a sign) what is known as the Feynman amplitude M in QED, QCD and the SM. We illustrate with a few topical examples. A detailed treatment can be found in Bjorken and Drell (1965) and in Cutler and Sivers (1978). 

The rules for calculating the Feynman amplitude M are essentially universal and irrespective of the normalization convention for the states. 

In (A2.1.6) is the modulus squared of the Feynman amplitude summed over final spins and colours and avers ed over initial spins and colours. 

A full and detmled calculation of a reaction rate, starting from a Feynman amplitude, is given in Section 8.6. 

For a Feynman amplitude, as computed directly from a Feynman diagram but without any spinors for the external lines, one has the following dimensional factors ... 

In the last step the symmetric covariants, are separated into 13 simpler terms, 5jT , given in table II of ref. [Tj87b], which also lists the values for Note that the positive and negative energy Feynman amplitudes are given by... 

Off-shell effects have been calculated using the IA2 model for proton-nucleus scattering at 200 and 500 MeV and found to be small [Ot 90a, Ot 90b, Ot 91]. This work is based on the factorized, off-shell IA2 optical potential in eq. (4.60) and uses fully off-shell Feynman amplitudes computed with the van Faassen and Tjon quasipotential meson exchange model, eq. (4.45). 

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