Multidimensional Dynamical Systems Accepting the Normal Shift

The dynamical systems of the form \ddot\bold r=\bold F (\bold r,\dot\bold r) in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force field \bold F(\bold r,\dot\bold r) of the dynamical systems with weak and complete normality are derived.Comment: AMS-TeX, ver. 2.1, IBM AT-386, size 16K (ASCII), short versio

The matrix Hamiltonian for hadrons and the role of negative-energy components

The world-line (Fock-Feynman-Schwinger) representation is used for quarks in arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green's function of the white $q\bar q$ system over gluon fields one obtains the relativistic Hamiltonian, which is matrix in spin indices and contains both positive and negative quark energies. The role of the latter is studied in the example of the heavy-light meson and the standard einbein technic is extended to the case of the matrix Hamiltonian. Comparison with the Dirac equation shows a good agreement of the results. For arbitrary $q\bar q$ system the nondiagonal matrix Hamiltonian components are calculated through hyperfine interaction terms. A general discussion of the role of negative energy components is given in conclusion.Comment: 29 pages, no figure

Analytic calculation of field-strength correlators

Field correlators are expressed using background field formalism through the gluelump Green's functions. The latter are obtained in the path integral and Hamiltonian formalism. As a result behaviour of field correlators is obtained at small and large distances both for perturbative and nonperturbative parts. The latter decay exponentially at large distances and are finite at x=0, in agreement with OPE and lattice data.Comment: 28 pages, no figures; new material added, misprints correcte

Contextual approach to quantum mechanics and the theory of the fundamental prespace

We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation has all distinguishing features of the quantum model. Thus in spite all ``No-Go'' theorems (e.g., von Neumann, Kochen and Specker,..., Bell) we found the realist basis for quantum mechanics. Our representation is not standard model with hidden variables. In particular, this is not a reduction of quantum model to the classical one. Moreover, we see that such a reduction is even in principle impossible. This impossibility is not a consequence of a mathematical theorem but it follows from the physical structure of the model. By our model quantum states are very rough images of domains in the space of fundamental parameters - PRESPACE. Those domains represent complexes of physical conditions. By our model both classical and quantum physics describe REDUCTION of PRESPACE-INFORMATION. Quantum mechanics is not complete. In particular, there are prespace contexts which can be represented only by a so called hyperbolic quantum model. We predict violations of the Heisenberg's uncertainty principle and existence of dispersion free states.Comment: Plenary talk at Conference "Quantum Theory: Reconsideration of Foundations-2", Vaxjo, 1-6 June, 200

Mixing of meson, hybrid, and glueball states

The effective QCD Hamiltonian is constructed with the help of the background perturbation theory, and relativistic Feynman--Schwinger path integrals for Green's functions. The resulting spectrum displays mass gaps of the order of one GeV, when additional valence gluon is added to the bound state. Mixing between meson, hybrid, and glueball states is defined in two ways: through generalized Green's functions and via modified Feynman diagram technic giving similar answers. Results for mixing matrix elements are numerically not large (around 0.1 GeV) and agree with earlier analytic estimates and lattice simulations.Comment: LaTeX2e, 23 pages, 4 Postscript figure