Higgsless electroweak model due to the spherical geometry

Abstract

A new formulation of the Electroweak Model with 3-dimensional spherical geometry in the target space is suggested. The free Lagrangian in the spherical field space along with the standard gauge field Lagrangian form the full Higgsless Lagrangian of the model, whose second order terms reproduce the same fields with the same masses as the Standard Electroweak Model. The vector bosons and electron masses are generated automatically, so there is no need in special mechanism.

Limiting case of modified electroweak model for contracted gauge group

“…We have discussed the limiting case of the modified Higgsless Electroweak Model [11]- [13], which corresponds to the contracted gauge group SU(2; j) × U(1), where j = ι or j → 0. The masses of the all experimentally verified particles involved in the Electroweak Model remain the same under contraction, but interactions of the fields are changed in two aspects.…”

“…The simple mechanism for generation of the vector boson masses in Electroweak Model was suggested in [11]- [13]. It is based on the fact that the quadratic form φ † φ = ρ 2 in the matter field space Φ 2 is invariant with respect to gauge transformations.…”

“…The vector boson masses are easy generated by the transformation of Lagrangian L(j = 1) (9) to the coordinates on the sphere S 3 . Higgs boson field does not appeared if the sphere radius does not depend on the space-time coordinates ρ = R = const [11]- [13]. For ρ = const the real positive massless scalar field -analogy of dilaton or kind of Goldstone mode -is presented in the model [15].…”

“…In a standard approach to generate mass terms for the vector bosons the "'sombrero"' potential is added to the matter field Lagrangian L φ (j = 1) (11) and after that the Higgs mechanism is used. The different way was recently suggested [11]- [13] and is based on the fact that the quadratic form φ † φ = ρ 2 is invariant with respect to gauge transformations. This quadratic form define the 3dimensional sphere S 3 of the radius ρ > 0 in the target space Φ 2 which is C 2 or R 4 if real components are counted.…”

“…And this is true for both values of the contraction parameter j = 1 and j = ι. If the sphere radius does not depend on the space-time coordinates ρ = R = const, then ∂ µ ρ = 0 and the real positive scalar field ρ as well as Higgs boson field are not present in the model [11]- [13]. In this case Lagrangian (36) describes massless vector fields A µ , m A = 0 (photon), massive vector field Z µ with the mass m Z = 1 2 R √ g 2 + g ′2 (Z-boson), massive vector fields W ± µ with identical mass m W = 1 2 gR (W-bosons) and interactions of these fields.…”