John C. Collins

Large order expansion in perturbation theory

Abstract We investigate the large n behavior of the perturbation coefficients En for the ground state energy of the anharmonic oscillator, considered as a field theory in one space-time dimension. We combine the saddle point expansion for functional integrals introduced in this context by Lipatov with the dispersion relation (in coupling constant) used by Bender and Wu. The complete Feynman rules for the expansion in 1 n are worked out, and we compute the first two terms, which agree with those computed by Bender and Wu using the WKB approximation. One feature of our analysis is a deformation of the integration contour in function space as one analytically continues in the coupling.

Renormalization of the Cottingham formula

Abstract The second-order electromagnetic contribution to the mass of a hadron needs an ultraviolet-divergent renormalization. An explicitly renormalized Cottingham formula is derived, and the renormalization is related to the counterterms obtained in perturbation theory. The main effect is to impose a cut-off Λ equal to the subtraction mass used in the renormalization. Within quantum chromodynamics it is shown that the Λ-dependence of the Cottingham formula for the neutron-proton mass difference is of the same magnitude as fourth-order electromagnetic corrections.

Large Order Expansion in Perturbation Theory

We investigate the large n behavior of the perturbation coefficients E n for the ground state energy of the anharmonic oscillator, considered as a field theory in one space-time dimension. We combine the saddle point expansion for functional integrals introduced in this context by Lipatov with the dispersion relation (in coupling constant) used by Bender and Wu. The complete Feynman rules for the expansion in 1/ n are worked out, and we compute the first two terms, which agree with those computed by Bender and Wu using the WKB approximation. One feature of our analysis is a deformation of the integration contour in function space as one analytically continues in the coupling.