Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

In this paper we present a summary of results obtained for scalar field theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED and chi^2phi theories are considered. The motivation behind the applications discussed in this paper is to use the FSR method as a rigorous tool for testing the quality of commonly used approximations in field theory. Exact calculations in a quenched theory are presented for one-, two-, and three-body bound states. Results obtained indicate that some of the commonly used approximations, such as Bethe-Salpeter ladder summation for bound states and the rainbow summation for one body problems, produce significantly different results from those obtained from the FSR approach. We find that more accurate results can be obtained using other, simpler, approximation schemes.Comment: 25 pags, 19 figures, prepared for the volume celebrating the 70th birthday of Yuri Simono

Quantum effective actions from nonperturbative worldline dynamics

We demonstrate the feasibility of a nonperturbative analysis of quantum field theory in the worldline formalism with the help of an efficient numerical algorithm. In particular, we compute the effective action for a super-renormalizable field theory with cubic scalar interaction in four dimensions in quenched approximation (small-$N_f$ expansion) to all orders in the coupling. We observe that nonperturbative effects exert a strong influence on the infrared behavior, rendering the massless limit well defined in contrast to the perturbative expectation. Our numerical method is based on a direct use of probability distributions for worldline ensembles, preserves all Euclidean spacetime symmetries, and thus represents a new nonperturbative tool for an investigation of continuum quantum field theory.Comment: 33 pages, 10 figure

The Generalized Gell-Mann--Low Theorem for Relativistic Bound States

The recently established generalized Gell-Mann--Low theorem is applied in lowest perturbative order to bound-state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann--Low Theorem retains, while being fully relativistic, many of the desirable features of the quantum mechanical approaches to bound states. In particular, no abnormal or unphysical solutions are found in the model under consideration. Both the non-relativistic and one-body limits are straightforward and consistent. The results for the spectrum are compared to those of the Bethe-Salpeter equation (in the ladder approximation) and related equations.Comment: 24 pages, 6 pspicture diagrams, 4 postscript figure

3-point off-shell vertex in scalar QED in arbitrary gauge and dimension

We calculate the complete one-loop off-shell three-point scalar-photon vertex in arbitrary gauge and dimension for Scalar Quantum Electrodynamics. Explicit results are presented for the particular cases of dimensions 3 and 4 both for massive and massless scalars. We then propose non-perturbative forms of this vertex that coincide with the perturbative answer to order $e^2$.Comment: Uses axodra

Bethe-Salpeter equation and a nonperturbative quark-gluon vertex

A Ward-Takahashi identity preserving Bethe-Salpeter kernel can always be calculated explicitly from a dressed-quark-gluon vertex whose diagrammatic content is enumerable. We illustrate that fact using a vertex obtained via the complete resummation of dressed-gluon ladders. While this vertex is planar, the vertex-consistent kernel is nonplanar and that is true for any dressed vertex. In an exemplifying model the rainbow-ladder truncation of the gap and Bethe-Salpeter equations yields many results; e.g., pi- and rho-meson masses, that are changed little by including higher-order corrections. Repulsion generated by nonplanar diagrams in the vertex-consistent Bethe-Salpeter kernel for quark-quark scattering is sufficient to guarantee that diquark bound states do not exist.Comment: 16 pages, 12 figures, REVTEX

Manifestation of three-body forces in three-body Bethe-Salpeter and light-front equations

Bethe-Salpeter and light-front bound state equations for three scalar particles interacting by scalar exchange-bosons are solved in ladder truncation. In contrast to two-body systems, the three-body binding energies obtained in these two approaches differ significantly from each other: the ladder kernel in light-front dynamics underbinds by approximately a factor of two compared to the ladder Bethe-Salpeter equation. By taking into account three-body forces in the light-front approach, generated by two exchange-bosons in flight, we find that most of this difference disappears; for small exchange masses, the obtained binding energies coincide with each other.Comment: 24 pages, 8 figures, submitted in Few-Body System

Nucleon-Nucleon Optical Model for Energies to 3 GeV

Several nucleon-nucleon potentials, Paris, Nijmegen, Argonne, and those derived by quantum inversion, which describe the NN interaction for T-lab below 300$ MeV are extended in their range of application as NN optical models. Extensions are made in r-space using complex separable potentials definable with a wide range of form factor options including those of boundary condition models. We use the latest phase shift analyses SP00 (FA00, WI00) of Arndt et al. from 300 MeV to 3 GeV to determine these extensions. The imaginary parts of the optical model interactions account for loss of flux into direct or resonant production processes. The optical potential approach is of particular value as it permits one to visualize fusion, and subsequent fission, of nucleons when T-lab above 2 GeV. We do so by calculating the scattering wave functions to specify the energy and radial dependences of flux losses and of probability distributions. Furthermore, half-off the energy shell t-matrices are presented as they are readily deduced with this approach. Such t-matrices are required for studies of few- and many-body nuclear reactions.Comment: Latex, 40 postscript pages including 17 figure

Unified approach to photo and electro-production of mesons with arbitrary spins

A new approach to identify the independent amplitudes along with their partial wave multipole expansions, for photo and electro-production is suggested,which is generally applicable to mesons with arbitrary spin-parity. These amplitudes facilitate direct identification of different resonance contributions.Comment: 11 page

Scalar-particle self-energy amplitudes and confinement in Minkowski space

We analyze the analytic structure of the Covariant Spectator Theory (CST) contribution to the self-energy amplitude for a scalar particle in a \phi^2 \chi-theory. To this end we derive dispersion relations in 1+1 and in 3+1 dimensional Minkowski space. The divergent loop integrals in 3+1 dimensions are regularized using dimensional regularization. We find that the CST dispersion relations exhibit, in addition to the usual right-hand branch cut, also a left-hand cut. The origin of this "spectator" left-hand cut can be understood in the context of scattering for a scalar \phi^2 \chi^2-type theory. If the interaction kernel contains a linear confining component, its contribution to the self-energy vanishes exactly.Comment: 19 pages, 11 figures; one paragraph added and some typos corrected; version published in Few-Body System