SHORT-RANGE AND LONG-RANGE FORCES IN QUANTUM THEORY: SELECTED TOPICS

Short-range forces (SRF) are encountered when the effects of the parity-violating (PV) weak neutral current are considered in atomic systems. We consider these and other SRF that are associated with operators that contain delta functions. Identities which convert a delta-function matrix element to that of a global operator are reviewed. Past and possible future applications of such identities are described. It has been found that use of these identities can substantially improve the results obtained with less accurate wave functions. We present a further application to the hyperfine structure of the ground state of lithium where we again find that results are improved by the use of an identity.;The transitions (gamma)+2('3)S(,1) (--->) 2('1)S(,0) and (gamma)+ 2('3)P(,0) (--->) 2('1)P(,1) in helium have been studied elsewhere in order to gain some insight into the reliability of approximate calculations which have been carried out for PV El transitions; the contributions of the nearest-lying states were computed with a variety of wave functions. Here we review this work and estimate the contribution of all singly-excited intermediate states by the use of a Green's function technique to carry out the sum over both bound and continuum states. We find that such contributions can be as large as 12% of those from near-lying states or as small as 1%. Therefore estimates of these contributions should be made on a case by case basis.;A long-range force (LRF) is here defined to be one that is associated with a potential V(r) that is asymptotically of the form (lamda)r('-1)(r(,0)/r)('N-1). We use a dispersion-theoretic approach to study LRF between hadrons due to two-gluon exchange within the framework of quantum chromodynamics. Such an LRF is usually related to the presence of a spectrum of physical states that extends to zero mass. A speculative scheme put forward by Feinberg and Sucher is used to avoid requiring the existence of massless gluons as observable particles. Semi-quantitative expressions for the two-gluon exchange potential between hadrons and, in particular, between two nucleons are obtained.;Limits on two-gluon corrections to (pi)p forward scattering dispersion relations are used to provide an upper bound for (lamda), the coupling constant in the nucleon-nucleon potential. For N > 7, expected on heuristic grounds, we obtain the bound (lamda) (LESSTHEQ) 10('6), which is very weak; gluon effects as treated here do not lead to significant effects in the dispersion-theoretic analysis of (pi)p scattering.;As preparation for a calculation concerning PV electric-dipole (El) transitions in helium, we review a theoretical framework for the calculation of neutral-current parity-mixing effects in many-electron atoms. The starting point is an external-field no-pair Hamiltonian H(,+) which allows for a consistent treatment of effects coming from virtual electron-positron pairs and can be used as a basis for a systematic program of calculations. A derivation of a practical formula for PV El transition matrix elements is summarized.