Limiting case of modified electroweak model for contracted gauge group

Abstract

The modification of the Electroweak Model with 3-dimensional spherical geometry in the matter fields space is suggested. The Lagrangian of this model is given by the sum of the free (without any potential term) matter fields Lagrangian and the standard gauge fields Lagrangian. The vector boson masses are generated by transformation of this Lagrangian from Cartesian coordinates to a coordinates on the sphere S 3 . The limiting case of the bosonic part of the modified model, which corresponds to the contracted gauge group SU (2; j) × U (1) is discussed. Within framework of the limit model Z-boson and electromagnetic fields can be regarded as an external ones with respect to W-bosons fields in the sence that W-boson fields do not effect on these external fields. The masses of all particles of the Electroweak Model remain the same, but field interactions in contracted model are more simple as compared with the standard Electroweak Model.

Natural limits of electroweak model as contraction of its gauge group

“…(1) × acts in the boson, lepton and quark sectors. The contracted group SU j (2; ) is obtained [12,13] by the consistent rescaling of the fundamental representation of SU (2) and the space C 2 z j jz z j j jz z u j z j…”

“…After transformations ( 27), (28) and spontaneous symmetry breaking the boson Lagrangian (2), (3) can be represented in the form [12,13] { } ( )…”

Natural limits of Electroweak Model as contraction of its gauge group

“…We consider a model where the contracted gauge group SU(2; j) × U(1) acts in the boson, lepton and quark sectors. The contracted group SU(2; j) is obtained [11,12] by the consistent rescaling of the fundamental representation of SU(2) and the space…”

“…where L b is Lagrangian of the base fields and L f is Lagrangian of the fiber fields. The boson Lagrangian L B (j) was discussed in [11,12] on the level of classical fields, where it was shown that masses of all particles involved in the Electroweak Model remain the same under contraction j 2 → 0. In this limit the contribution j 2 L f of neutrino, W -boson and u-quark fields as well as their interactions with other fields to the Lagrangian (24) will be vanishingly small in comparison with contribution L b of electron, d-quark and remaining boson fields.…”

“…In particular, the simple group SU( 2) is contracted to the nonsemisimple one SU(2; ι), which is isomorphic to the Euclid group E(2) = A 2 (×SO(1), where Abelian subgroup A 2 is generated by translations [11,12]. The fields space of the standard Electroweak Model is split after the contraction in such a way that neutrino, Wboson and u-quark fields are in the fiber, whereas all other fields are in the base.…”