Duration of interactions in quantum electrodynamics: basic concepts, temporal features of kinetic phenomena

TL;DR

This paper introduces a quantum field theory-based approach to defining temporal functions in QED, unifying delay and formation durations of scattering processes, and applies it to various kinetic phenomena and fundamental quantum concepts.

Contribution

It develops a general method to define temporal functions in QED using the Ward-Takahashi identity, linking them to kinetic theories and fundamental quantum processes.

Findings

Defines real and imaginary parts of temporal functions in QED

Reveals instanton-like nature of tunneling processes

Provides insights into adiabatic hypothesis and renormalization schemes

Abstract

For temporal magnitudes describing, in details, processes of particles scattering for a long time at each necessity case a particular, ad hoc reception were used. However the desirability of general approach basing on concepts of quantum field theory and uniting two main problems, durations of delay at scattering and of formation of arisen states, seems evident. We show that the Ward-Takahashi identity allows the defining of general temporal function in the frame of QED, real part of which describes the duration of delay of scattered particle on scatterer and imaginary part describes the duration of formation ("dressing") of outgoing bare particle. The functions of same form can be revealed in the known QED descriptions of processes, i.e. they arise in the course of standard calculations, but are not entered artificially. These functions submit to the operator of duration determinable by the reciprocal analogue of the Schroedinger equation, operator of which is canonically conjugated with Hamiltonian. Definition of temporal functions leads to the developing of such kinetic theories: theory of optical dispersion (with the decision of certain known paradoxes), theory of multiphoton processes (definitions of their thresholds and saturations) and theory of phase transitions (determination of general correlation radii and the full system of critical indices). The determination of temporal functions demonstrates also the instanton-type nature of tunneling processes, makes clear sense of the adiabatic hypothesis of quantum theory and some renormalization schemes. In an application to the problem of charge nullification they lead to a restriction of allowable number of fermions of the theory.