In the paper we consider the relationship between supersymmetric transformation of Hamiltonian and its dynamical constraints for some models of supersymmetric field theory. It is found that requirement of invariance of canonical Hamiltonian under global supersymmetry generates dynamical constraints of the model. For our examples, it is an alternative way to obtain the constraints (besides the Dirac–Bergmann algorithm). On the other hand, we have showed the invariance of these models on the surface of dynamical constraints.
Quantum theory of the gauge field with nonvanishing classical source is formulated in a way free of the gauge-choosing ambiguity. The special example of constant non Abelian classical field is considered in more detail. The tree propagators and one-loop action are explicitly calculated for this case.
Forward–backward correlations in high energy hadron–nucleus collisions are analyzed using a simple model that correctly describes correlations in hadron–hadron collisions. One finds that both in multiple scattering models and in “single effective scattering” models of hadron–nucleus interaction the main trends of the data are predicted correctly. However, more precise measurements should allow us to discriminate between models and to fix their free parameters.
The Heinz transport equations for \(q\bar q\) plasma are generalized to include a term responsible for \(q\bar q\) tunneling from vacuum in chromoelectric field. They are used to study the time dependence of the particle and energy densities and other characteristics of \(q\bar q\) production in a color flux tube. The energy density larger than 4 GeV/fm\(^3\) is found at the “formation time” 0.3 fm for a tube five times stronger than the elementary one. The oscillations of the system survive the damping effects brought about by the process of production of \(q\bar q\) pairs.
The quantum description of motion of a particle subjected to position-dependent frictional forces is presented. The approximation applied to solve the problem is especially good in the field of heavy-ion physics. The two cases are taken into account: a motion without external forces and a motion in the harmonic oscillator potential. As an example, a frictional barrier penetration is considered.