abstract

Null initial data techniques are used to describe the dynamics of classical Maxwell–Dirac fields in real Minkowski space. On the basis of the structure of the field equations a graphical device is constructed which enables one to unambiguously label elements of the corresponding infinite invariant exact set in terms of colored trees. The complete specification of the trees arises naturally from the procedures involved in the actual evaluation of the elementary contributions. Each tree turns out to be associated with a manifestly finite scaling invariant integral which is taken over a compact space of appropriate null configurations. In particular the integrals describing the processes of electromagnetic scattering of Dirac fields appear to be taken over spaces of forked null zigzags that start at the origin and terminate at a fixed point lying in the interior of the future cone of the origin.

abstract

We give a detailed account on the application of the Schwinger variational principle (SchVP) for the evaluation of operator Padé approximates (OPA’s). OPA’s can be considered in their simplest “one-loop” (ladder) form as solutions of scattering equations but allow for a more natural transition to quantum field theory beyond ladder approximation. Therefore methods for their evaluation are of high interest. One of these methods is the SchVP which we study in the special case of elastic nucleon–nucleon scattering in terms of the Blankenbecler–Sugar equation. Since exact proofs of convergence for the SchVP cannot be found in general, the intention of our paper is to give by a detailed study of this complex example a justification for the application of the SchVP in even more complex situations. Applying the SchVP, it is shown that relatively simple and quite precise approximations for the \(T\)-matrix elements can be constructed valid for the whole energy range under consideration.

abstract

The familiar analogy between the quantum time evolution of an isolated system and the thermal equilibrium of an open system with a thermostat is considered as a signal of a profound thermodynamic-type aspect of the physical time, suggesting small nonunitarity corrections to the conventional quantum theory. These imply, as their characteristic consequence, a tiny unitarity defect of \(S\) matrix. Another surprising consequence is a slight time dependence of mass of any matter system localized close to an experimental device such as a running supercollider or a big laser in action, where an intensive particle flow is produced. This suggests a described gedankenexperiment.

abstract

Intermittent correlations/fluctuations in the particle spectra of high-energy collisions are studied using correlation and fluctuation descriptions of cluster models. It is shown that leading contribution to intermittency in both methods may be connected with a cluster structure of multiparticle process.

abstract

An economy mass formula, found recently for leptons and quarks as a semiempirical relationship based on a Dirac square-root model proposed previously for three fermion families, is supplemented by an ansatz concerning four mass scales appearing in this formula (in four cases of neutrinos, charged leptons, up quarks and down quarks). Then, in the mass formula there remain only three free parameters that can be determined from experimental values of \(m_e\), \(m_{\mu }\) and |\(V_{us}\)|. Nevertheless, it predicts all other lepton and quark masses as well as quark mixing parameters in nice agreement with existing experimental data.

abstract

A model is presented describing quasi elastic and damped heavy ion collisions, at energies larger than 10 MeV/\(u\), as a process of stochastic nucleon and momentum transfer. Mass, energy, and angular distributions are calculated. The model allows also to evaluate dissipation of the entrance channel angular momentum. The effect of subsequent evaporation is included.