An exact solution of the Currie-Hill equations in 1 + 1 dimensional Minkowski space

We present an exact two-particle solution of the Currie-Hill equations of Predictive Relativistic Mechanics in $1 + 1$ dimensional Minkowski space. The instantaneous accelerations are given in terms of elementary functions depending on the relative particle position and velocities. The general solution of the equations of motion is given and by studying the global phase space of this system it is shown that this is a subspace of the full kinematic phase space.Comment: 13 pages, LaTeX. arXiv admin note: text overlap with arXiv:1402.699

Effective potential from zero-momentum potential

We obtain the centre-of-mass frame effective potential from the zero-momentum potential in Ruijsenaars-Schneider type 1-dimensional relativistic mechanics using classical inverse scattering methods.Comment: 24 pages, 10 figure

Bethe--Salpeter wave functions in integrable models

We investigate some properties of Bethe--Salpeter wave functions in integrable models. In particular we illustrate the application of the operator product expansion in determining the short distance behavior. The energy dependence of the potentials obtained from such wave functions is studied, and further we discuss the (limited) phenomenological significance of zero--energy potentials.Comment: LaTeX, 38 pages, 9 figure

Marchenko method with incomplete data and singular nucleon scattering

We apply the Marchenko method of quantum inverse scattering to study nucleon scattering problems. Assuming a $\beta/r^2$ type repulsive core and comparing our results to the Reid93 phenomenological potential we estimate the constant $\beta$, determining the singularity strength, in various spin/isospin channels. Instead of using Bargmann type S-matrices which allows only integer singularity strength, here we consider an analytical approach based on the incomplete data method, which is suitable for fractional singularity strengths as well.Comment: 20 pages, 8 figures, published versio

Neutron-proton scattering and singular potentials

We consider a Bargmann-type rational parametrization of the nucleon scattering phase shifts. Applying Marchenko's method of quantum inverse scattering we show that the scattering data suggest a singular repulsive core of the potential of the form $2/r^2$ and $6/r^2$ in natural units, for the ${}^3S_1$ and ${}^1S_0$ channels respectively. The simplest solution in the ${}^3S_1$ channel contains three parameters only but reproduces all features of the potential and bound state wave function within one percent error. We also consider the ${}^3S_1$-${}^3D_1$ coupled channel problem with the coupled channel Marchenko inversion method.Comment: 39 pages. Extended version. Title changed, presentation improved and a new appendix on the coupled channel problem adde

Walking in the 3-dimensional large NN scalar model

The solvability of the three-dimensional O($N$) scalar field theory in the large $N$ limit makes it an ideal toy model exhibiting "walking" behavior, expected in some SU($N$) gauge theories with a large number of fermion flavors. We study the model using lattice regularization and show that when the ratio of the particle mass to an effective 4-point coupling (with dimension mass) is small, the beta function associated to the running 4-point coupling is "walking". We also study lattice artifacts and finite size effects, and find that while the former can be sizable at realistic correlation length, the latter are under control already at lattice sizes a few ($\sim$3) correlation lengths. We show the robustness of the walking phenomenon by showing that it can also be observed by studying physical observables such as the scattering phase shifts and the mass gap in finite volume.Comment: 27 pages, 5 figures, typos in the published version are correcte

Structure functions of the 2d O(n) non-linear sigma models

We investigate structure functions in the 2-dimensional (asymptotically free) non-linear O(n) sigma-models using the non-perturbative S-matrix bootstrap program. In particular the exact small (Bjorken) x behavior is derived. Structure functions in the special case of the n=3 model are accurately computed over the whole x range for $-q^2/M^2<10^5$, and some moments are compared with results from renormalized perturbation theory. Some results concerning the structure functions in the 1/n approximation are also presented.Comment: 57 pages, 5 figures, 3 table

Flow equation for the large NN scalar model and induced geometries

We study the proposal that a $d+1$ dimensional induced metric is constructed from a $d$ dimensional field theory using gradient flow. Applying the idea to the O($N$) $\varphi^4$ model and normalizing the flow field, we have shown in the large $N$ limit that the induced metric is finite and universal in the sense that it does not depend on the details of the flow equation and the original field theory except for the renormalized mass, which is the only relevant quantity in this limit. We have found that the induced metric describes Euclidean Anti-de-Sitter (AdS) space in both ultra-violet (UV) and infra-red (IR) limits of the flow direction, where the radius of the AdS is bigger in the IR than in the UV.Comment: 21 pages, 2 figures. We dedicate this work to the memory of Peter Hasenfratz. The revised version for the publication of PTE