The Concept of Potential in Quantum Field Theory

TL;DR

This paper discusses the conceptual and practical aspects of defining potentials in quantum field theory, emphasizing the primary role of Lagrangian interactions and presenting a gauge-independent approach to bound state energies and two-photon exchange potentials.

Contribution

It introduces a gauge-independent method for analyzing bound states and reports recent findings on long-range two-photon exchange potentials.

Findings

Developed a gauge-independent approach to bound state energy calculations.

Presented new results on long-range two-photon exchange potentials.

Clarified the conceptual distinction between potentials and interactions in QFT.

Abstract

In quantum field theory the concept of a Lagrangian interaction density, expressed in terms of fields, is primary. Forces between two particles are regarded as arising primarily from the exchange of quanta of the bosonic fields. Thus, in contrast to nonrelativistic quantum mechanics, the concept of a two-body poten tial is secondary. Potentials are not given a priori but must be defined. Part of the purpose of this talk is to review and discuss the issues involved when such definitions are made. In this context I describe a gauge-independent approach to some aspects of the problem of determining the energy levels of bound states, developed in collaboration with the late G. Feinberg, and report some recent results on the long-range potential associated with two-photon exchange between charged particles.