On the unification of electroweak interactions with gravity

It is shown that the electroweak interactions in the Salam-Weinberg model can be described by a space-time connection form which preserves the space-time metric multiplied by a conformal factor. In addition, one needs an extraSO(2)-connection form. The Dirac field in this formalism is described (after making a certain regularity assumption) by a vierbein field for the space-time metric and a complex scalar field.Invited talk at the Intarnational Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–21, 1981.     

The standard model on non-commutative space-time: strong interactions included

This paper is a direct extension of our earlier work on electroweak currents and the Higgs sector in the standard model on non-commutative space-time, now with strong interactions included. Apart from the non-commutative corrections to standard model strong interactions, several new interactions appear. The most interesting ones are gluonic interactions with the electroweak sector. They are elaborated here in detail and the Feynman rules for interactions up to are provided.Received: 18 March 2005, Revised: 13 May 2005, Published online: 19 July 2005     

Strong unification

We investigate the possibility that unification occurs at strong coupling. We show that, despite the fact the couplings pass through a strong coupling regime, accurate predictions for their low energy values are possible because the couplings of the theory flow to infrared fixed points. We determine the low-energy QCD coupling in a favoured class of strong coupling models and find it is reduced from the weak coupling predictions, lying close to the experimentally measured value. We extend the analysis to the determination of quark and lepton masses and show that (even without Grand Unification) the infra-red fixed point structure may lead to good predictions for the top mass, the bottom to tau mass ratio and tan β. Finally we discuss the implications for the unification scale finding it to be increased from the MSSM value and closer to the heterotic string prediction.     

Gravitational and electroweak unification by replacing diffeomorphisms with larger group

The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers will agree whether any given quantity is conserved. Alternatively, and equivalently, it is defined by the assumption that all observers will agree that the general relativistic wave equation describes the propagation of light. Thus, the group replacement is analogous to the replacement of the Lorentz group by the diffeomorphisms that led Einstein from special relativity to general relativity, and is also consistent with the assumption of constant light velocity that led him to special relativity. The enlarged covariance group leads to a non-commutative geometry based not on a manifold, but on a nonlocal space in which paths, rather than points, are the most primitive invariant entities. This yields a theory which unifies the gravitational and electroweak interactions. The theory contains no adjustable parameters, such as those that are chosen arbitrarily in the standard model.     

The standard model on non-commutative space-time

We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter . No new particles are introduced; the structure group is . We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. Received: 29 November 2001 / Published online: 25 January 2002     

Some consequences of a non-commutative space-time structure

The existence of a fundamental length (or fundamental time) has been conjectured in many contexts. Here we discuss some consequences of a fundamental constant of this type, which emerges as a consequence of deformation-stability considerations leading to a non-commutative space-time structure. This mathematically well defined structure is sufficiently constrained to allow for unambiguous experimental predictions. In particular we discuss the phase-space volume modifications and their relevance for the calculation of the Greisen-Zatsepin-Kuz’min sphere. The (small) corrections to the spectrum of the Coulomb problem are also computed.Received: 23 December 2004, Revised: 18 April 2005, Published online: 8 July 2005PACS: 13.60.-r; 03.65.Bz; 98.70.Sa     

Semileptonic electroweak interactions with nucleons and nuclei

The basic formalism needed to describe parity-violating electron scattering from nucleons and nuclei is presented and the experiments anticipated in the next few years discussed. The underlying structure of the relevant leptonic and hadronic tensors is developed in some detail for both parity-conserving and -violating situations to highlight the new physics that becomes accessible in the latter case. When applying the basic formalism to specific (practical) examples, the theme of determining the strangeness content of the nucleon is stressed.Lectures given at the Indian-Summer School on Electron Scattering from Nucleous and Nuclei, Prague (The Czech Republic), September 1994.This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under cooperative agreement #DE-FC02-94ER40818.     

Neutrino dipole moments and charge radii in non-commutative space-time

In this paper we obtain a bound TeV on the scale of space-time non-commutativity considering photon-neutrino interactions. We compute *-dipole moments and *-charge radii originating from space-time non-commutativity and compare them with the dipole moments calculated in the neutrino-mass extended standard model (SM). The computation depends on the nature of the neutrinos, Dirac versus Majorana, their mass and the energy scale. We focus on Majorana neutrinos. The *-charge radius is found to be at TeV.Received: 17 June 2004, Published online: 18 August 2004     

Comment on triple gauge boson interactionsin the non-commutative electroweak sector

In this comment we present an analysis of electroweak neutral triple gauge boson couplings projected out of the gauge sector of the extended non-commutative standard model. A brief overview of the current experimental situation is given.Received: 31 July 2003, Published online: 20 November 2003     

Quantum weakdynamics as an SU(3)_I gauge theory: Grand unification of strong and electroweak interactions

Quantum weakdynamics (QWD) as an gauge theory with the vacuum term is considered to be the unification of the electroweak interaction as an gauge theory. The grand unification of beyond the standard model is established by the group . The grand unified interactions break down to weak and strong interactions at a new grand unification scale, GeV, through dynamical spontaneous symmetry breaking (DSSB); the weak and strong coupling constants are the same, , at this scale. DSSB is realized by the condensation of scalar fields, postulated to be spatially longitudinal components of gauge bosons, instead of Higgs particles. Quark and lepton family generation, the Weinberg angle , and the Cabbibo angle are predicted. The electroweak coupling constants are , , , and ; there are symmetric isospin interactions. Received: 21 January 2001 / Published online: 21 November 2001     

Gauge symmetries of electroweak interactions

By considering the symmetries associated with baryon number and lepton number conservation as gauge symmetries, the underlying gauge symmetry of weak electromagnetic interactions is shown to beSU(2) _L ×U(1)×U(1)Baryon×U(1)_Lepton. If right-handed currents exist on a par with the observed left-handed ones, then the full symmetry of electroweak interactions that emerges isSU(2)_L×SU(2)_R×U(1)_Baryon×U(1)_Lepton. These symmetries offer a rich spectrum of massive neutral gauge bosons, one of which is the massive neutral boson of the standardSU(2) _L ×U(1) _Y model.     

Fermion condensate model of electroweak interactions

A new dynamical symmetry breaking model of electroweak interactions is proposed based on interacting fermions. Two fermions of different SU_L(2) representations form a symmetry breaking condensate and generate the lepton and quark masses. The weak gauge bosons obtain their usual standard model masses from a gauge-invariant Lagrangian of a doublet scalar field composed of the new fermion fields. The new fermion fields become massive by condensation. It is shown that the new charged fermions are produced at the next linear colliders in large number. The model is a low-energy one, which cannot be renormalized perturbatively. For the parameters of the model, unitarity constraints are presented.     

No UV/IR mixing in unitary space-time non-commutative field theory

In this article we calculate several divergent amplitudes in -theory on non-commutative space-time ( ) in the framework of interaction-point time-ordered perturbation theory (IPTOPT), continuing work done in hep-th/0209253. On the ground of these results we find corresponding Feynman rules that allow for a much easier diagrammatic calculation of amplitudes. The most important feature of the present theory is the absence of the UV/IR mixing problem in all amplitudes calculated so far. Although we are not yet able to give a rigorous proof, we provide a strong argument for this result to hold in general. Together with the Feynman rules we found, this opens promising vistas onto the systematic renormalization of non-commutative field theories.Received: 26 August 2003, Published online: 20 November 2003V. Putz: Work supported by the Fonds zur Förderung der Wissenschaften (FWF) under contract P15015-TPH.