A general algorithm to construct particle trajectories in 1+1 dimensional canonical relativistic models is presented. The method is a generalization of the construction used in Ruijsenaars-Schneider models and provides a simple proof of the fact that
the latter satisfies the world-line conditions granting proper physical Poincare invariance. The 2-particle case for the rational Ruijsenaars-Schneider model is worked out explicitly. It is shown that the particle coordinates do not Poisson commute, as required by the no-interaction theorem of Currie, Jordan and Sudarshan.
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 p
article 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.
We review recent investigations on the short distance behaviors of potentials among baryons, which are formulated through the Nambu-Bethe-Salpeter (NBS) wave function. After explaining the method to define the potentials, we analyze the short distanc
e behavior of the NBS wave functions and the corresponding potentials by combining the operator product expansion and a renormalization group analysis in the perturbation theory of QCD. These analytic results are compared with numerical results obtained in lattice QCD simulations.
Hybrid-NLIE equations, an alternative finite NLIE description for the spectral problem of the super sigma model of AdS/CFT and its gamma-deformations are derived by replacing the semi-infinite SU(2) and SU(4) parts of the AdS/CFT TBA equations by a f
ew appropriately chosen complex NLIE variables, which are coupled among themselves and to the Y-functions associated to the remaining central nodes of the TBA diagram. The integral equations are written explicitly for the ground state of the gamma-deformed system. We linearize these NLIE equations, analytically calculate the first correction to the asymptotic solution and find agreement with analogous results coming from the original TBA formalism. Our equations differ substantially from the recently published finite FiNLIE formulation of the spectral problem.
We present a method of removing all infinite sums from the various forms of the mirror TBA equations and the energy formula of the AdS/CFT spectral problem. This new formulation of the TBA system is quasi-local because Y-functions that are connected
by the TBA equations are at most next to nearest neighbors with respect to the Y-system diagram of AdS/CFT.
Lattice artifacts in the 2d O(n) non-linear sigma-model are expected to be of the form O(a^2), and hence it was (when first observed) disturbing that some quantities in the O(3) model with various actions show parametrically stronger cutoff dependenc
e, apparently O(a), up to very large correlation lengths. In a previous letter we described the solution to this puzzle. Based on the conventional framework of Symanziks effective action, we showed that there are logarithmic corrections to the O(a^2) artifacts which are especially large, (ln(a))^3, for n=3 and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O(3) and O(4) are also presented.
