Natural limits of electroweak model as contraction of its gauge group

Abstract

The low and higher energy limits of the electroweak model are obtained from the first principles of gauge theory. Both limits are given by the same contraction of the gauge group, but for the different consistent rescalings of the field space. Mathematical contraction parameter in both cases is interpreted as energy. Very weak neutrino–matter interactions are explained by zero tending contraction parameter, which depends on neutrino energy. The second consistent rescaling corresponds to the higher energy limit of the electroweak model. At the infinite energy all particles lose mass, electroweak interactions become long-range and are mediated by neutral currents. The limit model represents the development of the early Universe from the big bang up to the end of the first second.

Elementary particles in the early Universe

“…It follows from Lagrangian L( ) = L q ( ) + L gl ( ), that the total reconstruction of the quark color degrees of freedom will take place after the restoration of all quark masses (≈ 2 ) at the same time with the reestablishment of all electroweak interactions (≈ 4 ). Complete color interactions start to work later because some of them are proportionate to the eighth power 8 .…”

“…Then we use the fact that the electroweak epoch starts at the temperature T 4 = 100 GeV (1 GeV = 10 13 K) and the QCD epoch begins at T 8 = 0, 2 GeV. In other words we assume that complete reconstruction of the EWM, whose Lagrangian has minimal terms proportionate to 4 , and QCD, whose Lagrangian has minimal terms proportionate to 8 , take place at these temperatures. Let us denote by ∆ the cutoff level for k , k = 1, 2, 4, 6, 8, i.e.…”

Integrable potentials on Cayley-Klein spaces from quantum groups

“…But when contraction of some mathematical structure is performed one can reconstruct the initial structure by the deformation in the narrow sense moving back along the contraction way. Similar approach was used to describe the early history of the Universy starting from the electroweak model [9]. Hamiltonians in the base H I z,b (j 1 , ι 2 ) (27) and H I z,b (ι 1 , ι 2 ) (21) are obtained namely in this way.…”

Study of information entropy for involved quantum models in complex Cayley-Klein space

“…Several applications are also evident in their review, including the generalization of integral Hamiltonians with an explicit dependence of the constant curvature on the 2D curved spaces, which are ultimately interpreted as anisotropic or isotropic oscillators [18][19][20][21] depending on the fixed amount of contraction from Cayley-Klein space. In another application of the contraction, we refer to the contraction-induced of the gauge group, which are yielded based on the gauge theory, the higher and lower limits of energy from electroweak models because of the contraction [22].…”