Perturbative Results Without Diagrams

Higher-order perturbative calculations in Quantum (Field) Theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature from the cumulant expansion of the corresponding observable followed by an extrapolation to zero temperature. This method (originally proposed by Bogolyubov and Plechko) is applied to the calculation of higher-order terms for the ground-state energy of the polaron. Using state-of-the-art multidimensional integration routines 2 new coefficients are obtained corresponding to a 4- and 5-loop calculation.Comment: 6 pages, 2 figures, WS style (included), to be published in Proceedings of "Path Integrals - New Trends and Perspectives", Dresden (Germany), Sept. 23 - 28, 200

Vacuum Polarization Effects in the Worldline Variational Approach to Quantum Field Theory

The worldline variational approach is extended beyond the quenched approximation, i.e. to include virtual pair production of heavy particles. This is achieved either by an expansion of the functional determinant to second order or by an hybrid ansatz for the quadratic trial action consisting of fields for the light particles and worldlines for the heavy ones as in the linear polaron model. Numerical results and analytic approximations show a reduction of radiative effects with increasing number of flavors.Comment: 3 pages, 2 figures, to be published in the proceedings of PANIC05, Santa Fe, NM, USA, Oct. 200

Nuclear Polarization Corrections for the S--Levels of Electronic and Muonic Deuterium

We calculate the second-order corrections to the atomic energy level shifts in ordinary and muonic deuterium due to virtual excitations of the deuteron which are important for ongoing and planned precise experiments in these systems. For light atoms a method can be used in which the shift is expressed as integrals over the longitudinal and transverse inelastic structure functions of the nucleus. We employ the structure functions arising from separable NN potentials of the Yamaguchi and Tabakin form which can be evaluated analytically. Special emphasis is put on gauge invariance which requires a consistent inclusion of interaction currents and seagull terms. The effect of the D-wave component of the deuteron is investigated for the leading longitudinal contribution. We also estimate the shift for pionic deuterium.Comment: 11 pages (plain latex), one figure available by request, PSI-PR-93-16 (to appear in Phys. Let. B

Proton Polarization Shifts in Electronic and Muonic Hydrogen

The contribution of virtual excitations to the energy levels of electronic and muonic hydrogen is investigated combining a model-independent approach for the main part with quark model predictions for the remaining corrections. Precise values for the polarization shifts are obtained in the long-wavelength dipole approximation by numerically integrating over measured total photoabsorption cross sections. These unretarded results are considerably reduced by including retardation effects in an approximate way since the average momentum transfer (together with the mean excitation energy) turns out to be larger than usually assumed. Transverse and seagull contributions are estimated in a simple harmonic oscillator quark model and found to be non-negligible. Possible uncertainties and improvements of the final results are discussed.Comment: 8 pages, LATEX, no figures, discussion improved and references updated, final version accepted for publication in Phys. Lett.

Improved variational description of the Wick-Cutkosky model with the most general quadratic trial action

We generalize the worldline variational approach to field theory by introducing a trial action which allows for anisotropic terms to be induced by external 4-momenta of Green's functions. By solving the ensuing variational equations numerically we demonstrate that within the (quenched) scalar Wick-Cutkosky model considerable improvement can be achieved over results obtained previously with isotropic actions. In particular, the critical coupling associated with the instability of the model is lowered, in accordance with expectations from Baym's proof of the instability in the unquenched theory. The physical picture associated with a different quantum mechanical motion of the dressed particle along and perpendicular to its classical momentum is discussed. Indeed, we find that for large couplings the dressed particle is strongly distorted in the direction of its four-momentum. In addition, we obtain an exact relation between the renormalized coupling of the theory and the propagator. Along the way we introduce new and efficient methods to evaluate the averages needed in the variational approach and apply them to the calculation of the 2-point function.Comment: 32 pages, 4 figures, Latex. Some typos corrected and expanded discussion of the instability of the model provided. Accepted in Eur. Phys. J.

A New Path-Integral Representation of the TT-Matrix in Potential Scattering

We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the $T$-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious variables as was necessary before. The resulting expression serves as a starting point for a variational approximation applied to high-energy scattering from a Gaussian potential. Good agreement with exact partial-wave calculations is found even at large scattering angles. A novel path-integral representation of the scattering length is obtained in the low-energy limit.Comment: 9 pages, 1 figure, Latex with amsmath, amssym; v2: some typos corrected, matches published versio