Regular Series


Vol. 22 (1991), No. 7, pp. 595 – 665


On a Transformation Property of the Smoluchowski Aggregation Equation

abstract

Using a specific time-reversal transformation, the Smoluchowski equation for aggregation processes is proved to be formally equivalent to the equation obeyed by the partition function of random cascading models of multiparticle production processes with intermittent fluctuations. This result gives an unexpected connection between intermittent patterns of fluctuations, spin-glass systems and the dynamics of aggregation and gelling, first described for brownian motion by Smoluchowski already 75 years ago.


Running Couplings and the Higgs Boson Mass

abstract

We consider upper bounds on the Higgs boson mass based on the perturbative unitarity and an Argand diagram analysis. The bounds show a maximum sensitivity of 10–20 0eV when different running Higgs boson couplings are used.


An Example of \(N\)-Body Quantum-Mechanical Model That Eludes the Second Quantization

abstract

A quantum-mechanical system of \(N\) spin-\({}^1\!/\!{}_2\) identical particles, where \(\gamma \) matrices anticommute for different particles, is shown to escape the procedure of the second quantization (in the physical space). Instead, a quantization procedure in the Fock configurational space, called here the third quantization, is outlined. The respective particles are referred to as the non-Abelian Dirac particles. A system of \(N\) such particles, tightly concentrated around its centre of mass, can always be described in the pointlike limit by the Dirac equation corresponding to a composite, reducible (for \(N \gt 1\)) representation of the Dirac algebra. According to a previous discussion by the author, such representations with \(N = 1,3,5\) may be responsible for the puzzling phenomenon of three fermion generations, if an intrinsic exclusion principle is introduced.

See Erratum Acta Phys. Pol. B 23, 83 (1992)


Inversion of the Fermionic Matrix and Multigrid

abstract

Numerical simulations indicate that the multigrid method has some natural limitations when applied to the calculation of the quark propagator in the Lattice QCD.


Estimates for a Hypothetical Magnetic-Type Interaction of Nucleons

abstract

The new magnetic-type interaction for nucleons, following from a hypothetical Abelian composite structure of quarks is further discussed. A particular model is explored, where the quark is composed of a spin-\({}^1\!/\!{}_2\) preon (existing in two flavors) and a spin-0 preon (existing in three colors) bound together by a new Abelian gauge field producing a Coulombic attraction \(V = -e^{\rm (u)2}/r\) with \(O(e^{(u)2})=1\). Denoting the resulting new magnetic-type moment of the nucleon by \(\mu ^{\rm (u)}_{\rm N} = 3e^{\rm (u)}_{\rm eff}/2m_{\rm N}\), we are able to show that \(9e^{\rm (u)}_{\rm eff} \ll e^{\rm (u)2}\). Hfs experiments for H\(_2\) molecules set the upper limit \(9e^{\rm (u)}_{\rm eff} \lt 2 \times 10^{-7}\). The ordinary magnetic moment of the nucleon comes out \(\mu _{\rm N} = (3\) or \(-2)e/2m_{\rm N}\) for \(N = p\) or n, in good agreement with the experiment.


The Elementary Method in Pairing Energy. I. The Like Particles

abstract

The elementary method in pairing energy calculations has been presented: (i) for like-nucleons in the \(j\)–\(j\) coupling; (ii) for like nucleons in the \(l\)–\(s\) coupling; (iii) for bosons on the degenerated \(l\)—level. The simple explanation how and, more involved why the elementary method works has also been given.


Nuclear Transients

abstract

Nuclear scattering is classically analysed using realistic conservative interactions. Due to chaoticity of motion, the projectile can stay in the vicinity of the target for a long time. Such phenomena are called transients. We investigate properties of transients: fractal dimensions, Lyapunov exponents and mean lifetimes. We conclude that the lifetime of transients is similar to that of single-particle resonances. It rises substantially when we consider a more general system, with larger number of degrees of freedom.


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