Regular Series


Vol. 20 (1989), No. 10, pp. 829 – 898


Kinks Under Constant Forces

abstract

The behaviour of two-dimensional kinks under constant forces is fully analyzed in this paper. The most general solution is found and shown to be equivalent to the two-dimensional “bounce” in asymmetric potentials. The conditions under which the solution hereby presented behaves as an oscillating elliptic kink are also discussed.


Cosmic Strings in Extra-U(1) Model

abstract

In this work a cosmic string arising as a result of spontaneous breaking of the SU(2)\(_{\rm L} \times {\rm U}(1)_{\rm Y} \times {\rm U}(1)_{\rm E}\) symmetry is investigated.


Dirac Equation with Hidden Extra Spins: A Generalization of Kähler Equation

abstract

It is observed that the Dirac anticommutation relations admit some peculiar reducible representations implying the existence of additional spins 1/2 commuting with the usual spin 1/2 and being decoupled from the magnetic field in the Dirac equation. In the case of the simplest representation of this class the Dirac equation becomes equivalent to the Kähler equation. So, such, a class of reducible representations gives a generalization of Kähler equation, realizing the Dirac square-root procedure in the case of arbitrary total spin. A possible relation of the generalized Kähler equation to the problem of fermion generations is sketched.


On the Equivalence of Different Definitions of \(R\)-Operation

abstract

Three well-known definitions of R-operation in the BPHZ formalism are presented. The equivalence between the Zimmermann’s forest formula and the factorized version of \(R\)-operation is proved.


A Decuplet for g\(_{\rm T}\) Mesons

abstract

Assuming that g\(_{\rm T}\) mesons belong to a meson decuplet, we predict the masses of its nonisosinglet members. We discuss how the accuracy of the prediction depends on the experimental errors of the masses of g\(_{\rm T}\) mesons. We note, that the present errors are such that the prediction would be drastically improved, if they were slightly reduced. We calculate also the octet contents of g\(_{\rm T}\) mesons as functions of one parameter and conclude that none of them is excluded as glueball candidate, if only g\(_{\rm T}\) masses are known.


Remarks on the Multiplicity Measure for \(e^+e^-\) Annihilation

abstract

A recent proposal of the Lund group suggesting a multiplicity measure for \(e^+e^-\) annihilation is analyzed. It is shown that the results obtained for the multiplicity distributions in full phase space do not change if one removes a questionable assumption of exact localization of branching products in rapidity (thus avoiding troubles for small rapidity bins). The predicted asymptotic form of the distribution is shown to differ from the negative binomial distribution.


Modelling of Narrow Air Showers

abstract

Calculations are made for the distributions of central densities (of electromagnetic particles) by integrating over radii \(R \approx 0.4\) m and \(R \approx 0.8\) m, and for the spectrum over the total number of particles in a shower, as well as for the distributions of the fractions of the total number of particles in a detector exhibiting maximum count rate setting the thresholds to be \(N_{\rm c} \geq 170\) and \(N_{\rm c} \geq 625\) particles. Comparison with the experimental data is performed.


On the Absence of the Temperature Phase Transition in Finite Supersymmetric Gut’s

abstract

It is shown that temperature phase transition does not take place in supersymrnetric finite GUT’s. An example of such theory is given.


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