Exchange amplitudes and dispersion relations for electron-atom scattering

The analytic structure of the second Born approximation to the forward elastic exchange amplitude is analyzed for e^?+H scattering, and the importance of the interplay between bound and continuum intermediate state contributions is emphasized.     

Concentratable functionals and asymptotic relations for scattering amplitudes

Very wide classes of concentratable functionals are considered, i.e. classes where the notion of concentrating, which satisfies a certain six axioms, can be introduced, and where it is possible to formulate the microcausality (or the local-commutativity) principle as the requirement of concentration of functionals in the corresponding space-time region. Every such class of functionals is essentially wider than the class of tempered distributions and is defined on some analytic functions only. It is proved that the asymptotic smoothed partially-microcausal amplitude of an arbitrary reaction, under corresponding conditions imposed only in the physical region of changing arguments, satisfies all the asymptotic relations.     

Gluon cascades and amplitudes in light-front perturbation theory

We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.     

Invariant amplitudes and double dispersion relations for electron-muon scattering

For electron-muon scattering, a set of six invariant amplitudes free from kinematical singularities is determined. A simple proof of this freedom is given. Projection operators for this set are constructed. Double dispersion relations using natural subtraction points are derived for the box diagram.     

Renormalization group and relations between scattering amplitudes in a theory with different mass scales

In the Yukawa model with two different mass scales, the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. By considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives the possibility to reduce the problem to the scattering of light particles in the “external field” substituting a heavy virtual state. Applications of the results to problems of searches for new physics beyond the Standard Model are discussed.     

Diagrammatic operator formalism for string amplitudes

A diagrammatic operator method based on Fock space formulations of 3-string vertices is developed for computing the integration measure for open or closed string S-matrix to arbitrary loop order. The proposed vertex does not triangulate the moduli space, thus a single diagram incorporates a number of string field theory diagrams. However, the formalism does not naturally lead to a single cover of moduli space, and the restriction to the fundamental domain must be put in by hand, as in the Polyakov functional integral approach.     

Scattering amplitudes of QCD string in the worldline formalism

I review the derivation of large-N QCD meson scattering amplitudes in the Regge regime, where the effective theory of long strings applies in d = 4. A special attention is payed to the reparametrization path integral which plays a crucial role in the consistency of off-shell amplitudes. I show how the linear Reggeon trajectory is obtained for QCD string in the mean-field approximation, which turns out to be exact for the Nambu-Goto string, and discuss the interrelation with perturbative QCD.     

Analytic proton-nucleus scattering amplitudes

Analytic expressions for the elastic nucleon-nucleus amplitudes F(q) and G(q) are derived. They are based on analytic approximations of the nuclear profile functions in the Glauber formulation. Our amplitudes are sums of terms with a familiar structure, black-sphere Bessel functions multiplied by form factors accounting for the diffuseness of the nuclear surface. Their accuracy is tested with the Woods-Saxon density and found to be excellent for momentum transfers q? 5fm^?1.     

Recursion relations for the multi-Veneziano amplitude and the residue functions

It is shown that the multi-Veneziano amplitude is the generating function of multiple partitions. Recursion relations for the multi-Veneziano amplitude and the residue functions are explicitly given.     

Reciprocity relations for reflected amplitudes

We derive general reciprocity relations that are applicable to a large class of one-dimensional stratified systems. These results reveal clearly the role of absorption and spatial symmetry in the nonreciprocity of reflection observed in a recent experiment by Armitage et al. [Phys. Rev. B 58, 15, 376 (1998)]. We also present examples of structures for which such nonreciprocal effects can be significant.     

Poles and zeros in ππ scattering amplitudes

We draw attention to the remarkable systematics exhibited in the ππ amplitudes provided by the CERN-Munich data. It is shown that the existence of resonance poles with specific spin and mass values and the behaviours of the amplitude zeros in the Mandelstam plane give strong support to the ideas associated with dual resonance models. It is emphasized that some gauge-like conditions of dual resonance models play an essential role in these considerations.