Intermediate Sums Research Articles

Hard-Pion Current-Algebra Calculation of meson Processes—Three-Point Functions

Hard-pion techniques are presented for calculating vertex functions involving $\ensuremath{\pi}$, $\ensuremath{\rho}$, ${A}_{1}$, and $\ensuremath{\sigma}$ mesons. The development of the method involves the following assumptions: (a) saturation of intermediate sums by single mesons, (b) chiral $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ algebra commutation relations, (c) conservation of vector current, and (d) partial conservation of axial-vector current.

Infrared contributions to intermediate state sums in quantum electrodynamics

A method has been developed for incorporating the Bloch-Norsdsieck approximation into intermediate state sum expansions in quantum electrodynamics, so as to explicitly include the contributions of soft photons to these sums. This accomplishes the removal of infrared divergences usually incurred in approximations involving the cutting off of such intermediate state sums, and in addition, within the framework of such approximations, gives strong high energy convergence properties to the theory. The formalism developed is applied to modify Fainberg's work on quantum electrodynamic dispersion relations (1). An asymptotic form for the electron's charge form factor is derived, and is shown to be consistent with second order perturbation theory, and a series expansion for the charge renormalization constant Z 3 is obtained, all of whose terms are finite, except for those which arise from states containing only hard photons and no pairs. In a separate development, a comparison is made of the various methods which have been developed for treating the radiative corrections to scattering cross sections due to soft photons.

Infrared contributions to intermediate state sums in quantum electrodynamics: R. Perrin and E. L. Lomon. Department of Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts

Infrared contributions to intermediate state sums in quantum electrodynamics: R. Perrin and E. L. Lomon. Department of Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts