Fermion Pair Production Research Articles

Radiative correction to the equivalent-photon spectrum of a relativistic electron and the two-photon process.

On the basis of the improved Weizsaecker-Williams equivalent-photon spectrum of a fast charged particle, we calculate the radiative correction to this spectrum. The calculation involves the virtual-photon radiative correction, the soft- and hard-bremsstrahlung contributions, and the vacuum-polarization contribution. The results are used to calculate the radiative correction to two-photon production of neutral bosons and pair production of charged fermions and bosons. General features are that the elastic vertex radiative corrections to these processes are negative and large, up to 10--20%, while the total radiative corrections, including emission of an extra hard photon, are on the other hand positive and in general considerably smaller, of the order of 1%. The effect of electron tagging on the radiative corrections is briefly discussed.

Production of fermion pairs associated with decay of a metastable vacuum

A study is made of the production of fermion pairs associated with the tunneling process that leads to decay of a metastable vacuum in field theory. The technique of nonunitary Bogolyubov transformations is developed. Expressions are obtained for the spectrum of the produced fermions. The spectrum of fermion pairs produced when there is homogeneous decay of a metastable vacuum is found as an example.

Improved Weizsäcker-Williams method

In the spirit of the Weizs\"acker-Williams method virtual-photon spectra are derived which have the Weizs\"acker-Williams form for low frequencies. It is shown for the cases of pair production of fermions and single-boson production that the photon spectra give remarkably accurate results for one- and two-virtual-photon processes.

Operator Calculus in Quantized Field Theory

Following the suggestion of Feynman, we analyze the operators corresponding to the electron-positron field by means of the operator calculus. Thus we can deduce operationally Feynman's theory from the second quantized theory. With the aid of the external spinors, which are considered as the analogues of the Schwinger's prescribed source, we obtain formally a closed form of the S-matrix. Using this result we can derive the diffusion equation for the Dirac field very simply. The relations to the Schwinger's new theory of Green function are also discussed. Finally the formula for multiple boson or fermion pair-production are presented as illustrations for applications.