Other Possible Games in Town: Part 2

Nonlinear Theory of Elementary Particles: I. Choice of Axiomatics and Mathematical Apparatus of Theory (by Alexander G. Kyriakos): Abstract: In the previous paper (http://prespacetime.com/index.php/pst/article/viewFile/14/11), which can be considered as an introduction to the nonlinear theory, we have shown that the Standard Model (SМ) is not an axiomatic, but an algorithmic theory. In the proposed article the simplest (minimal) axiomatics is examined from the point of view of the possible forms of its mathematical representation. http://prespacetime.com/index.php/pst/article/view/30

"Electroweak Forces" Acting on TE, TM & TEM (by Giuliano Bettini)

Abstract: We have shown previously that the energy impulse four-vector of the propagating electromagnetic field inside a waveguide and in free space can be described by a Dirac spinor. This suggests an analogy with, for example, TE-electron, TM-positron and possibly TEM-neutrino. The aim of this work is an interpretation of the action, if any, of the electroweak gauge group SU(2)xU(1) on the before-mentioned e.m. fields (TE, TM & TEM modes). This is based on the following observation: The energy impulse four-vector is invariant under a global transformation of SU(2)xU(1), so the Dirac spinor can be “gauged” in order to verify not only the effect of the electromagnetic forces but also the weak forces. In other words, what are “weak forces”, if any, on TE, TM and TEM? Obviously this requires a modification of the Dirac equation to accommodate the larger gauge group. This is in fact done here, and it is shown that the analogous of the “weak forces” can be roughly interpreted in the following way: The W boson acts as a (receiving or transmitting) horn antenna, performing the transformation TEM ←→ TE, TM, giving or subtracting mass to the field; the Z° boson is as a radar target acting on the TEM (neutrinos) with a Doppler frequency. These objects have mathematical counterparts in gauge fields. No Higgs boson is needed in the theory. http://prespacetime.com/index.php/pst/article/view/31

Equivalent Waveguide Representation for Dirac Plane Waves (by Giuliano Bettini)

Abstract: Ideas about the electron as a sort of a bound electromagnetic wave and/or the electron as electromagnetic field trapped in a (equivalent) waveguide can be found more or less explicitly in many papers. What we want to show here is that the Dirac equation for electron and positron plane waves admits an equivalent electrical circuit, consisting of an equivalent transmission line. The same transmission line is representative of a mode in waveguide, so one can also say that the Dirac equation for plane waves includes an implicit representation in terms of an equivalent waveguide. All calculations will be carried out in elementary form with the usual notations of circuit theory and electromagnetism and without the need to resort to Clifford algebra as in previous papers. http://prespacetime.com/index.php/pst/article/view/32

Radar Scattering as "Gauge Theory" (by Giuliano Bettini)

Abstract: A preliminary attempt is made in this paper to construct a spinor theory of radar scattering or radar signal-target interaction as gauge theory in quantum mechanics. In this “gauge theory” of radar scattering radar signals and radar targets may become visible macroscopic objects to be put in analogy with Standard Model particles and interactions. The basic idea is that particles and forces are all of electromagnetic nature, light, and appear different due to the size and shape of interacting objects. For the purpose of this paper, one needs first to deal with a generic radar signal in spinor form. This is done by deriving a spinor representation of the TE and TM through the Dirac equation for plane waves, starting rigorously from Maxwell's equations without any use of equivalent V, I in electrical circuits. The representation is then extended to TEM. Then I introduce a tentative procedure to express the deflection of the field in a different direction, and its variation in frequency, and rest mass. This is accomplished through the interaction with SU(2)xU(1) gauge fields, i.e., electroweak interactions. Some simple but illustrative examples are given. Of course, the ideas set out here need further research. http://prespacetime.com/index.php/pst/article/view/33

The Modern Analysis of the Problem of Multisecting an Angle (by Temur Kalanov)

Abstract: The work is devoted theoretical and practical analysis of an actual problem – the problem of multisecting (in particular, trisecting) an angle, i.e. the problem of division of a given arbitrary angle into the given set of equal parts using only a compasses and an unmarked straightedge. General statement of a problem is formulated. The mathematical analysis of the problem (within the framework of the theories of similarity of triangles and of similarity of concentric circles) and the logical analysis of the problem are proposed. It is proved that practical solution of the problem of multisecting an arbitrary angle with only a compasses and an unmarked straightedge is impossible because an arc cannot be transformed to the straight line segment with a compasses and a straightedge. http://prespacetime.com/index.php/pst/article/view/34