abstract

Construction of the symplectic connection on phase space is proposed. This connection is in a sense defined by the Riemannian connection on the configuration space. The generalized Moyal product leading to the quantum multiplication in the curved phase space is given.

abstract

Master equations governing the probability densities of the stochastic processes driven by explicitly non-Markovian dichotomic noise are derived and discussed. Such equations form the infinite hierarchy of equations for different probability densities or correlation functions defined at more and more time points. Approximations introducing decoupling of such hierarchies are constructed. Applications to special cases: random telegraph process and linear relaxation show that one class of approximations leads in these cases to correct (exact) results.

abstract

It is argued that the observed deficit of solar and atmospheric neutrinos can be explained by neutrino oscillations \(\nu _e \rightarrow \nu _s \) and \(\nu _\mu \rightarrow \nu '_{s}\) involving two hypothetic sterile neutrinos \(\nu _s \) and \(\nu '_{s} \) (blind to all Standard–Model interactions). They are keen to mix nearly maximally with \(\nu _{e}\) and \(\nu _{\mu }\), respectively, to form neutrino mass states \(\nu _1\), \(\nu _4 \) and \(\nu _2 \), \(\nu _5 \). Our argument is presented in the framework of a model of fermion “texture” formulated previously, which implies the existence of two sterile neutrinos beside the three conventional.

abstract

We carry out a gauge independent Hamiltonian analysis of the CP\(^1\) model coupled to the Hopf term. We show that no fractional spin is revealed at the classical level — a result that is different from the corresponding case for the O(3) nonlinear sigma model. We next show that if the former model is altered through an identity involving the time derivative, an expression of fractional spin emerges at the classical level itself, which is given in terms of the soliton number of the model. This result matches several other existing results, both for the CP\(^1\) as well as the sigma model versions, obtained through canonical or path integral quantization.

abstract

The intermittency analysis of single event data (particle moments) in multiparticle production is improved, taking into account corrections due to the reconstruction of history of a particle cascade. This approach is tested within the framework of the \(\alpha \)-model.

abstract

We study the question whether the pole-model VMD approach to weak radiative hyperon decays can be made consistent with Hara’s theorem and still yield the pattern of asymmetries characteristic of the quark model. It is found that an essential ingredient which governs the pattern of asymmetries is the assumed off-shell behaviour of the parity-conserving \(1/2^--1/2^+-\gamma \) amplitudes. It appears that this behaviour can be chosen in such a way that the pattern characteristic of the quark model is obtained, and yet Hara’s theorem satisfied. As a byproduct, however, all parity-violating amplitudes in weak radiative and nonleptonic hyperon decays must then vanish in the SU(3) limit. This is in conflict with the observed size of weak meson–nucleon couplings.

abstract

In a dilute system of instantons and antiinstantons, the U\(_{\rm A}\)(1) and scale anomalies are shown to be directly related to the bulk susceptibility and compressibility of the system. Using \(1/N_{ c}\) (where \(N_{ c}\) is the number of colors) as a book-keeping argument, mesonic, baryonic and gluonic correlators are worked out in \(p\)-space and Fourier transformed to \(x\)-space for a comparison with recently simulated correlators. The results are in overall agreement with simulations and lattice calculations, for distances up to 1.5 fm, despite the fact that some channels lack the necessary physical singularities. We analyze various space-like form factors of the nucleon and show that they are amenable to constituent quark form factors to leading order in \(1/N_{ c}\). Issues related to the lack of confinement in the model and its consequence on the various correlation functions and form factors are also discussed.

abstract

The odderon equation is studied in terms of the variable suggested by the modular invariance of the 3 Reggeon system. Odderon charge is identified with the cross-product of three conformal spins. A complete set of commuting operators: \(\hat {h}^2\) and \(\hat {q}\) is diagonalized and quantization conditions for eigenvalues of the odderon charge \(\hat {q}\) are solved for arbitrary conformal weight \(h\).

abstract

It is shown that the recently established strong mass-dependence of the radii of the hadron sources, as observed in HBT analyses of the \(e^+e^-\) annihilation, can be explained by assuming a generalized inside–outside cascade, i.e. that (i) the four-momenta and the space-time position four-vectors of the produced particles are approximately proportional to each other and (ii) the “freeze-out” times are distributed along the hyperbola \(t^2-z^2= \tau _0^2\).

abstract

The parton content of the electron is analyzed within perturbative QCD. It is shown that electron acquires an anomalous component from QCD, analogously to photon. The evolution equations for the ‘exclusive’ and ‘inclusive’ electron structure function are constructed and solved numerically in the asymptotic \(Q^2\) region.

abstract

The analysis of the statistical and dynamical fluctuations in nucleus-nucleus collisions on an event-by-event basis strongly relies on a comparison with specially constructed artificial events where statistical fluctuations and kinematical correlations are under control. In this paper, we present a novel, analytical method of constructing reference events based on independent emission, modified by the energy/momentum constraint, which can lead to a better understanding of the nature of the observed final-state fluctuations. This approach can be easily used in the analysis of other topics in the heavy ion field (e.g. flow, HBT etc.) allowing more precise measurements.