Second-order integrable Lagrangians and WDVV equations

Letters in Mathematical Physics - We investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $\begin{aligned} \int...     

Studying pion effects in the quark propagator

Within the framework of Schwinger-Dyson and Bethe-Salpeter equations we investigate the importance of pions for the quark-gluon interaction. To this end we choose a truncation for the quark-gluon vertex that includes intermediate pion degrees of freedom and adjust the interaction such that unquenched lattice results for various current quark masses are reproduced. After extrapolation to the physical point we find a considerable contribution of the pion back reaction to the quark mass function as well as to the chiral condensate.     

Correlation effects in pion condensates

The threshold for pion condensation in neutron star matter is estimated on the basis of a sufficiently realistic treatment of effective forces. It turns out that the short range repulsion of the nucleon-nucleon force raises considerably the density at which the pion condensed phase can occur.     

Instanton effects in matrix models and string effective Lagrangians

We perform an explicit calculation of the lowest order effects of single eigenvalue instantons on the continuous sector of the collective field theory derived from a d = 1 bosonic matrix model. These effects consist of certain induced operators whose exact form we exhibit.     

Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics

We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler–Poincaré (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then state the EP Averaging Result—that GLM equations arise from GLM Hamilton’s principles in the EP framework. Next, we derive a new set of approximate small-amplitude GLM equations (gℓm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the gℓm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The gℓm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction (WMFI). The gℓm EP motion equations for compressible and incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or gℓm) fluid theory with a Taylor hypothesis closure (THC). Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha closure equations. We use the EP Averaging Result to bridge between the GLM equations and the Euler-alpha closure equations. Hence, combining the small-amplitude approximation with THC yields in new turbulence closure equations for compressible fluids in the EP variational framework.     

Calculation of superpropagators in non-linear quantum field theories

A new method of constructing the superpropagators, i.e. the Fourier transforms of the expressions of the form is suggested. The method makes it possible to derive by use of the same technique explicit analytic expressions for the superpropagators for a wide class of field theories — from strictly local up to essentially non-local. The essence of the method is the construction of a differential equation for the superpropagator which in general is of an infinite order. By use of the boundary condition atp ²=0 we find the solution of this equation depending on one arbitrary real parameter. Simple examples are given to illustrate the method.     

RPA correlation effects in radiative pion capture

A sum rule approach to radiative pion capture is given in terms of the energy-weighted and inverse-energy weighted sum rules. They are evaluated with RPA accuracy for Skyrme-like interactions. The static polarizabilities of the dipole, quadrupole and octupole isovector modes turn out to be the relevant quantities to determine the total branching ratios and mean photon energies.     

Non-locality effects on the pion nucleon form factor

We investigate effects of the non-locality in the elementary pion quark coupling on theπNN form factor in the framework of the chiral bag model. We show that this nonlocality leads to shorter ranged form factors thereby reducing the discrepancy between large bag-model confinement radii and empirically found small-ranged cut-off parameters.     

Studying pion effects on the chiral phase transition

We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a 5% change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed.     

Fermi sea effects on pion and kaon properties in the Nambu-Jona-Lasinio model

We study modifications of hadronic properties in dense nuclear and neutron matter, in the context of a generalized three-flavor Nambu-Jona-Lasinio model, focussing mainly on Fermi sea effects. In symmetric nuclear matter, we observe the splitting between K^± and the occurrence of a low-lying K⁻ branch at baryonic densities around 0.4 times normal nuclear matter density ϱ₀. This branch is not significantly affected by the inclusion of strange matter in the medium while the flavor asymmetry is preserved. A similar π⁺ branch is found in neutron matter at neutron densities around 0.3ϱ₀. These low-lying modes are particle-hole excitations of the Fermi sea and decrease smoothly with density. In any case, the vacuum does not exhibit signs of instability associated with boson condensation.     

Lagrangian averages,averaged Lagrangians,and the mean effects of fluctuations in fluid dynamics

We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.     

Incoherent pion photoproduction on the deuteron including polarization effects

Incoherent pion photoproduction on the deuteron including polarization effects is studied in the energy region from π-threshold up to the Δ(1232)-resonance with inclusion of all leading πNN effects. For the elementary pion photoproduction operator, a realistic effective Lagrangian approach is used which displays chiral symmetry, gauge invariance, and crossing symmetry, as well as a consistent treatment of the spin-3/2 interaction. The interactions in the final two-body subsystems are taken in separable form. Effects of final state interaction are investigated and their role in unpolarized and polarization observables are found to be significant. The extracted cross sections and spin asymmetries are compared with available experimental data and predictions of other works, and a satisfactory agreement is obtained. In addition, the sensitivity of results to the elementary N(γ, π)N operator is investigated. Considerable dependence of the d(γ, π)NN results on the elementary amplitude is found. This indicates that it can serve as a filter for different elementary operators.