abstract

The nonrelativistic (NR) shell model of nuclei based on one-particle states results in a “surprise” pointed out by Peierls, which consists in the accelerated motion of “free” nucleus impossible to eliminate by the standard perturbation theory. The NR mechanics solves the puzzle by indicating a geometrically privileged position of the absolute configuration space generated by the three-dimensional space R\(_3\) spanned on the relative coordinate “\(y\)”. This converts the “\(n\)-body” problem into the “\((n-1)\)-relational-object” problem with absolute (frame-independent) structures. The relativistic kinematics shows that the Galilean-absolute characteristics of the system obtained in the \(\overbrace {{\rm R}_3 \times \dots \times {\rm R}_3}^{n-1}\) configuration space remain absolute in the true Minkowskian spacetime L\(_4\) of measurement. However, this necessitates abandoning the classical L\(_4\)-eventism as the first metrical continuum of physics.

abstract

Algebraic spinor spaces in the Clifford algebras of two- and four-dimensional Minkowski spaces are considered. Their description in terms of primitive idempotens and their classification with respect to the action of the Lorentz group are given.

abstract

It is shown that Einstein–Yang–Mills-dilation theory has a countable family of static globally regular solutions which are purely magnetic but uncharged. The discrete spectrum of masses of these solutions is bounded from above by the mass of extremal Gibbons–Maeda solution. As follows from linear stability analysis all solutions are unstable.

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For nonlinear systems which can be described using simple generic forms of kinetic equations, with a priori unspecified but still present internal and parametric fluctuation terms, it is possible to extract noise characteristics from simple experimental data. Several examples are provided to illustrate this point.

abstract

We describe two Monte Carlo algorithms for simulation of QED radiative processes in deep inelastic \(e^{\pm } p \to e^{\pm } X\) scattering. One of them, implemented in the program LESKO-F, includes \(\mathcal {O}(\alpha )\) QED radiative corrections. The other one describes multiphoton leptonic radiation in a framework of the Yennie–Frautschi–Suura exclusive exponentiation procedure and is a base of the program LESKO-YFS. Some numerical results of the above Monte Carlo programs are presented. We also comment on including QCD effects and hadronization in the both programs. Next, we discuss a problem of unfolding QED radiative corrections from the data. We present two methods of reducing hard photon radiation effects in the low \(x\) region. In one of them tagging hard radiative photons almost collinear with the incident electrons is used to estimate a non-radiative cross section. Experimental aspects of photon tagging are also discussed. The other method exploits information from a measurement of both final state electron and hadrons energies and angles to tag and reject hard initial radiation photon events. Some toy models of electron and hadron detectors are considered in this study. Both methods allow to reduce significantly QED radiative effects and can be used to extract the proton structure function at HERA. Finally, we argue that an effect of a reduction of an effective electron beam energy due to hard initial state photon radiation can be used to measure the longitudinal structure function at HERA. Results of a Monte Carlo simulation including statistical accuracy and systematic effects are presented.

abstract

Superfluid phase transition in He\(^4\) can be accomplished through pressure quench on a short (dynamical) timescale. “Vacuum condensate” of the new, broken symmetry phase is the wavefunction of the superfluid Bose condensate with a certain “trapped” distribution of vortex lines. Analogous phase transitions from the false to the true vacuum are expected to occur in the early universe. There they are thought to leave behind topological defects such as strings. I calculate the density of strings (i.e., vortex lines) predicted by the application of the cosmological scenario to He\(^4\). The proposed experiment tests key elements of the standard cosmological scenario for creation of topological defects — known as the Kibble mechanism — in a cryogenic setting. Analogous experiments can be performed in superconductors as well as in either phase of He\(^3\), and have been already carried out by Yurke and his co-workers in liquid crystals.