No abstract

This work presents new round of the author's pursuit for consistent description of the finite sized objects in classical and quantum field theory. Current paper lays out an adequate mathematical background for this quest. A novel framework of the matter-induced physical affine geometry is developed. Within this framework, (1) an intrinsic nonlinearity of the Dirac equation becomes self-explanatory; (2) the spherical symmetry of an isolated localized object is of dynamic origin; (3) the auto-localization is a trivial consequence of nonlinearity and wave nature of the Dirac field; (4) localized objects are split into two major categories that are clearly associated with the positive and negative charges; (5) of these, only the former can be stable as isolated objects, which explains the global charge asymmetry of the matter observed in Nature. In the second paper, the nonlinear Dirac equation is written down explicitly. It is solved in one-body approximation (in absence of external fields). Its two analytic solutions unequivocally are positive (stable) and negative (unstable) isolated charges. From the author's current perspective, the so for obtained results must be developed further and applied to various practical and fundamental problems in particle and nuclear physics, and also in cosmology.

We study the dynamics of quantum fluctuations which take place at the earliest stage of highenergy processes and the conditions under which the data from e-p deep-inelastic scattering may serve as an input for computing the initial data for heavy-ion collisions at high energies. Our method is essentially based on the space-time picture of these seemingly different phenomena. We prove that the ultra-violet renormalization of the virtual loops does not bring any scale into the problem. The scale appears only in connection with the collinear cut-off in the evolution equations and is defined by the physical properties of the final state. In heavy-ion collisions the basic screening effect is due to the mass of the collective modes (plasmons) in the dense non-equilibrium quark-gluon system, which is estimated. We avoid the standard parton phenomenology and suggest a dedicated class of evolution equations which describe the dynamics of quantum fluctuations in heavy ion collisions.12.38. Mh, 12.38.Bx, 24.85.+p,

Using the general framework of quantum field theory, we derive basic equations of quantum field kinetics. The main goal of this approach is to compute the observables associated with a quarkgluon plasma at different stages of its evolution. We start by rewriting the integral equations for the field correlators in different forms, depending on the relevant dynamical features at each different stage. Next, two versions of perturbation expansion are considered. The first is best suited for the calculation of electromagnetic emission from chaotic, but not equilibrated, strongly interacting matter. The second version allows one to derive evolution equations, which are generalizations of the familiar QCD evolution equations, and provide a basis for the calculation of the initial quark and gluon distributions after the first hard interaction of the heavy ions.

We derive expressions for various correlators of the gauge field and find the propagators in Hamiltonian dynamics which employs a new gauge A τ = 0. This gauge is a part of the wedge form of relativistic dynamics suggested earlier as a tool for the study of quantum dynamics in ultrarelativistic heavy ion collisions. We prove that the gauge is completely fixed. The gauge field is quantized and the field of radiation and the longitudinal fields are unambiguously separated. The new gauge puts the quark and gluon fields of the colliding hadrons in one Hilbert space and thus allows one to avoid factorization.