Electroweak Theory With a Minimal Length

Abstract

According to the introduction of a minimal length to quantum field theory which is directly related to a generalized uncertainty principle the implementation of the gauge principle becomes much more intricated. It has been shown in another paper how gauge theories have to be extended in general, if there is assumed the existence of a minimal length. In this paper this generalization of the description of gauge theories is applied to the case of Yang-Mills theories with gauge group SU (N ) to consider especially the application to the electroweak theory as it appears in the standard model. The modifications of the lepton-, Higgs-and gauge field sector of the extended Lagrangian of the electroweak theory maintaining local gauge invariance under SU (2)L ⊗ U (1)Y transformations are investigated. There appear additional interaction terms between the leptons or the Higgs particle respectively with the photon and the W-and Z-bosons as well as additional self-interaction terms of these gauge bosons themselves. It is remarkable that in the quark sector where the full gauge group of the standard model, SU (3)c ⊗ SU (2)L ⊗ U (1)Y , has to be considered there arise coupling terms between the gluons und the W-and Z-bosons which means that the electroweak theory is not separated from quantum chromodynamics anymore.

Relativistic generalized uncertainty principle

“…This effectively chooses a special frame of reference, bringing back the notion of an aether. Because of this difficulty, GUP models so far have been mainly considered in non-relativistic theories with few attempts in relativistic theories and quantum field theory [18][19][20][21][22][23][24][25][26][27][28]. In the present work, we study this aspect and propose a Lorentz covariant GUP which reduces to its familiar non-relativistic versions at low energies, and incorporates a minimum length.…”

Deformation of the Wheeler–DeWitt equation

“…In this new Heisenberg algebra commutation relations between position and momentum operators contain momentum dependent factors. It may be noted that the implications of this modified uncertainty principle for quantum field theory have also been studied [24]- [26].…”

Short distance physics of the inflationary de Sitter universe

“…It is possible to generalize the gauge principle for theories with a minimum length scale [53], which is done by first analyzing the full spacetime deformation caused by the generalized uncertainty principle, and then converting all the derivatives in the theory to gauge covariant derivatives. Such a generalization for the electroweak sector of standard model has also been performed in [54]. It will be interesting to use this theory to study the Higgs inflation with a minimum length scale.…”