β Scribed by Nicolas Papanicolaou
No coin nor oath required. For personal study only.
We present a formal calculation of the infrared singularity structure of the fermion propagator in QED based on the Faddeev-Kulish asymptotic solution. The Renormalization program is reviewed in the context of the BPHZ subtraction scheme and a refinement of the Renormalization group methods is employed to study the infrared singularities in perturbation theory.
There is a renewed interest on the infrared problem in QED after the work of Chung [I], Kibble [2], Fadeev and Kulish [3], and Zwanziger [4]. The substantial ingredient in these works is the attempt to define a finite S-matrix for the theory. This led to the introduction of "coherent states" as the appropriate states for the description of the asymptotic dynamics. The consistency of these treatments relies upon justification of the results obtained, in renormalized perturbation theory. In particular, the use of coherent states is consistent with power-law singularity structure of the Green Functions as the momenta approach the mass-shell values [2], [4]. It is then of particular importance to know the infrared structure of Green's functions, which is a highly nonperturbative aspect of the theory. For this reason many of the existing treatments, initiated by the classical work of Bloch and Nordsieck [S], are formal. In particular, they fall into two main categories. In the first one, we deal with a certain type of approximations, which do not affect the Green functions near the mass-shell values of the momenta. These methods are deficient in the sense that one formally manipulates unrenormalized quantities so that neither the approximations nor the operational calculus are justified. The literature in this direction is very extensive to be cited here. We selectively refer to the work of Kibble [2], where the infrared structure of all Green's functions was calculated by summing leading terms in perturbation theory (leading in the sense of powers of logarithms).
π SIMILAR VOLUMES
In view of extending the shell model to highly deformed states of heavy nuclei, we discuss the evaluation of the Green's function for the Schrodinger equation in three dimensions with a smooth potential, in the limit of large quantum numbers. Such an evaluation is possible only after smoothing over
One-particle propagators of the relativistic electron-positron gas are systematically investigated. With the nonvanishing chemical potential the neutrality of the whole system is secured by a uniformly charged classical background described by a classical current J,,. Due to the translational invari