abstract

We consider particles carrying both the electric and magnetic charges in the Yang–Mills theory. The Hamiltonian formulation for the system has been carried out in the Coulomb gauge. The zero mode problem associated with the Coulomb gauge has been taken care of by introducing generalized Green’s functions and imposing the restrictions of orthogonality of source terms and zero modes. It has been shown that the orthogonality imposes restrictions on the physical states of the system.

abstract

The Yang–Mills field equations in presence of extended electric and magnetic sources have been considered and the solutions have been obtained by formulating the equations as an initial value problem in temporal gauge. For spherically symmetric electric and magnetic source distributions, the totally screened solutions with arbitrary low energy have been obtained. The static solutions for the non-spherically symmetric sources have also been obtained.

abstract

It is studied to what extent the QED bremsstrahlung effects may obscure the experimental verification of the standard electroweak theory by means of measuring quantities/distributions related to \(\tau \) spin polarization in the \(\tau \) production process around the Z\(_0\) resonance. In the presented investigation the following effects are taken into account: single hard bremsstrahlung from \(e^{\pm }\) and \(\tau ^{\pm }\), leading one loop corrections of the standard theory, longitudinal spin polarization of \(e^{\pm }\) and the spin polarization effects in \(\tau ^+\tau ^-\) decays. All numerical results are obtained using a Monte Carlo event generator for the combined \(\tau ^{\pm }\) production and decay process. It is shown that the radiative effects are definitely less sizable on the top of \(Z_0\) than off the peak. They depend strongly on kinematical cut-offs used to eliminate the hard bremsstrahlung effects. Also a number of analytical calculations are presented, notably a new simple parametrization of the hard bremsstrahlung spin amplitudes.

abstract

The spherically symmetric Yang–Mills theory with GSU(2) gauge supergroup is analysed. The solution is found consisting of electric and magnetic monopoles coupled with some scalar anticommuting field. Long range terms \((\sim \frac {1}{r}\ {\rm if}\ r \to \infty )\) appear in the electric and magnetic fields.

abstract

The Lund string model is used in estimation of the average time needed for the formation of final hadrons in high energy collisions. The energy-dependence of the formation time and sensitivity of results to the choice of the scaling function of the model is studied.

abstract

The Bogoliubov–Valatin variational technique is used to describe chiral symmetry breaking in QCD with a finite baryonic number density at zero temperature. Using the BCS-like trial vacuum state with the condensate wave function approximated by \(\sim \exp (-1/2 R^2(k-\alpha K_{\rm F})^2)\) with a different from zero, it is shown that the chirally invariant vacuum is unstable for small baryonic density. Our results also indicate that in the high. baryonic density regime chiral symmetry is restored, presumably in the first order phase transition.

abstract

In Skyrme model with 3 flavors the limit \(N_{\rm C} \to \infty \) is explicitly performed. Mass splittings and magnetic moments for the baryonic states in such a model are calculated and compared with the data.

abstract

Dilatation effect of life-times of “micro-clocks” shows a controversy between the relativistic and quantum symmetries connected with quantum nonlocality that has recently bean discussed in connection with Bell’s inequalities violation. This controversy can be overcome within the hypothesis of internal spacetime R\(_4\) of “relations” by making “events” of Minkowskian spacetime L\(_4\) analyzable.

abstract

Activity composition was measured for soil contaminated with the fallout from the Chernobyl accident. The soil samples were collected at various areas of Poland. A map showing the \(^{137}\)Cs deposit distribution was drawn for the most contaminated southern part of Poland.