arXiv subjects

H. B. Nielsen

Publications and source records attributed to H. B. Nielsen.

At least 127 records · Page 7Linked to original sources

arXiv2001

Lorentz Invariance and Origin of Symmetries

In this letter we reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can only be imposed in the sense that all Lorentz non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. Remarkably, the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the appearance of a symmetry and, what is more, to the massless vector fields gauging this symmetry in both Abelian and non-Abelian cases. In contrast, purely global symmetries are only generated as accidental consequences of the gauge symmetry.

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arXiv2001

Phase Transition Couplings in U(1) and SU(N) Regularized Gauge Theories

Using a 2-loop approximation for $β$-functions, we have considered the corresponding renormalization group improved effective potential in the Dual Abelian Higgs Model (DAHM) of scalar monopoles and calculated the phase transition (critical) couplings in U(1) and SU(N) regularized gauge theories. In contrast to our previous result $α_{crit} \approx 0.17$, obtained in the one-loop approximation with the DAHM effective potential (see Ref.[20]), the critical value of the electric fine structure constant in the 2-loop approximation, calculated in the present paper, is equal to $α_{crit}\approx 0.208$ and coincides with the lattice result for compact QED [10]: $α_{crit}^{lat} \approx 0.20\pm 0.015$. Following the 't Hooft's idea of the "abelization" of monopole vacuum in the Yang--Mills theories, we have obtained an estimation of the SU(N) triple point coupling constants, which is $α_{N,crit}^{-1}=\frac{N}{2}\sqrt{\frac{N+1}{N-1}} α_{U(1),crit}^{-1}$. This relation was used for the description of the Planck scale values of the inverse running constants $α_i^{-1}(μ)$ (i=1,2,3 correspond to U(1), SU(2) and SU(3) groups), according to the ideas of the Multiple Point Model [16].

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arXiv2001

Phase Transition in the Higgs Model of Scalar Fields with Electric and Magnetic Charges

Using a one-loop renormalization group improvement for the effective potential in the Higgs model of electrodynamics with electrically and magnetically charged scalar fields, we argue for the existence of a triple (critical) point in the phase diagram ($λ_{run}, g_{run}^4$), where $λ_{run}$ is the renormalised running selfinteraction constant of the Higgs scalar monopoles and $g_{run}$ is their running magnetic charge. This triple point is a boundary point of three first-order phase transitions in the dual sector of the Higgs scalar electrodynamics: The "Coulomb" and two confinement phases meet together at this critical point. Considering the arguments for the one-loop approximation validity in the region of parameters around the triple point A we have obtained the following triple point values of the running couplings: $(λ_{(A)}, g^2_{(A)})\approx(-13.4; 18.6)$, which are independent of the electric charge influence and two--loop corrections to $g^2_{run}$ with high accuracy of deviations. At the triple point the mass of monopoles is equal to zero. The corresponding critical value of the electric fine structure constant turns out to be $α_{crit} = π/g^2_{(A)}\approx{0.17}$ by the Dirac relation. This value is close to the $α_{crit}^{lat}\approx{0.20\pm 0.015}$, which in a U(1) lattice gauge theory corresponds to the phase transition between the "Coulomb" and confinement phases. In our theory for $α\ge α_{crit}$ there are two phases for the confinement of the electrically charged particles. The results of the present paper are very encouraging for the Anti--grand unification theory which was developed previously as a realistic alternative to SUSY GUTs. The paper is also devoted to the discussion of this problem.

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arXiv2001

Standard Model Higgs Boson Mass from Borderline Metastability of the Vacuum

We have studied imposing the condition that the Standard Model effective Higgs potential should have two approximately degenerate vacua, such that the vacuum we live in is just barely metastable: the one in which we live has a vacuum expectation value of 246 GeV and the other one should have a vacuum expectation value of order the Planck scale. Alone borderline metastability gives, using the experimental top quark mass 173.1 \pm 4.6 GeV, the Higgs mass prediction 121.8 \pm 11 GeV. The requirement that the second minimum be at the Planck scale already gave the prediction 173\pm 4 GeV for the top quark mass according to our 1995 paper.

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arXiv2001

Neutrino mass matrix in Anti-GUT with see-saw mechanism

We have investigated the predictions of neutrino oscillations within extended Anti-GUT, based on a large gauge group - the Standard Model and an B-L abelian group assumed with separate gauge fields coupling to each family of quarks and leptons. We take into account corrections concerning a crude way of accounting for the number of ways the vacuum expectation values of the Higgs fields of the model can be ordered in the Feynman diagrams yielding the mass matrix elements. Performing these corrections in a balanced way between the charged fermion sector and the neutrino sector (case I) leads to the previous version of our model that was a fit to the MSW small angle solution region. The fit considered here is marginally worse that the previous fit inasmuch as it predicts a somewhat lower solar neutrino mass square difference (which might though be the only way of avoiding the day-night exclusion region). The other two versions (case II and case III) are characterised by the heaviest of the see-saw neutrino matrix elements that are composed either of ν_{Rμ} and ν_{Rτ} or two ν_{Rτ}. These cases II and III fit the small mixing angle MSW scenario very well.

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arXiv2001

Baryogenesis via lepton number violation in Anti-GUT model

We study the baryogenesis via lepton number violation in the model of Anti-GUT. The origin of the baryogenesis is the existence of right-handed Majorana neutrinos which decay in a C, CP and lepton number violation way. The baryon number asymmetry is calculated in the extended Anti-GUT model which is only able to predict order of magnitude-wise. We predicted baryon number to entropy ratio, Y_B=1.46{+5.87\atop-1.17}\times10^{-11}, and this result agrees with experimental values very well.

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arXiv2001

A Neutrino Mass Matrix Model with many Quantum charges and No SUSY

We present a model based on our favourite gauge group which we call Anti-GUT and which in its extended form to be applied for neutrinos in the see-saw picture consists in that we have for each family separately a set of gauge fields as in the Standard Model plus a gauged (B-L)-charge. It may function as a concrete model manifestation of the type of model suggested by some general statistical considerations as to what a mass matrix model is to be to match naturally the rough features of the spectrum and the baryon asymmetry so nicely obtained in see-saw models along the Fukugita-Yanagida scheme.

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arXiv2000

Neutrino Oscillations in Extended Anti-GUT Model

What we call the Anti-GUT model is extended a bit to include also right-handed neutrinos and thus make use of the see-saw mechanism for neutrino masses. This model consists in assigning gauge quantum numbers to the known Weyl fermions and the three see-saw right-handed neutrinos. Each family (generation) is given its own Standard Model gauge fields and a gauge field coupled to the $B-L$ quantum number for that family alone. Further we assign a rather limited number of Higgs fields, so as to break these gauge groups down to the Standard Model gauge group and to fit, w.r.t. order of magnitude, the spectra and mixing angles of the quarks and leptons. We find a rather good fit, which for neutrino oscillations favours the small mixing angle MSW solution, although the mixing angle predicted is closest to the upper side of the uncertainty range for the measured solar neutrino mixing angle. An idea for making a ``finetuning''-principle to ``explain'' the large ratios found empirically in physics, and answer such questions as ``why is the weak scale low compared to the Planck scale?'', is proposed. A further very speculative extension is supposed to ``explain'' why we have three families.

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arXiv2000

Why odd-space and odd-time dimensions in even-dimesional spaces?

We are answering the question why 4-dimensional space has the metric 1+3 by making a general argument from a certain type of equations of motion linear in momentum for any spin (except spin zero) in any even dimension d. All known free equations for non-zero spin for massless fields belong to this type of equations. Requiring Hermiticity(This is a generalization of an earlier work which shows that without assuming the Lorentz invariance -which in the present work is assumed- the Weyl equation follows using Hermiticity.) of the equations of motion operator as well as irreducibility with respect to the Lorentz group representation, we prove that only metrics with the signature corresponding to q time + (d - q) space dimensions with q being odd exist. Correspondingly, in four dimensional space, Nature could only make the realization of 1+3 dimensional space.

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arXiv2000

Neutrino mass matrix suppression by Abelian charges with see-saw mechanism

We have investigated a neutrino mass matrix model without supersymmetry including three see-saw right-handed neutrinos around order $10^{12}$ GeV masses, aiming at a picture with all small numbers explained as being due to approximately conserved gauge charges. The prediction of the solar neutrino mixing angle is given by $\sin^22θ_{\odot}= 3 {+3\atop -2}\times10^{-2}$; in fact, the solar mixing angle is, apart from detailed order unity corrections, equal to the Cabibbo angle. Furthermore the ratio of the solar neutrino mass square difference to that for the atmospheric neutrino oscillation is predicted to $6 {+11\atop -4}\times10^{-4}$ and is given by the same Cabibbo angle related parameter $ξ$ as $6 ξ^4$.

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arXiv2000

The Majorana particles and the Majorana sea

Can one make a Majorana field theory for fermions starting from the zero mass Weyl theory, then adding a mass term as an interaction? The answer to this question is: yes we can. We can proceed similarly to the case of the Dirac massive field theory. In both cases one can start from the zero mass Weyl theory and then add a mass term as an interacting term of massless particles with a constant (external) field. In both cases the interaction gives rise to a field theory for a free massive fermion field. We present the procedure for the creation of a mass term in the case of the Dirac and the Majorana field and we look for a massive field as a superposition of massless fields.

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arXiv2000

Unification of spins and charges in Grassmann space and in space of differential forms

Polynomials in Grassmann space can be used to describe all the internal degrees of freedom of spinors, scalars and vectors, that is their spins and charges. It was shown that Kähler spinors, which are polynomials of differential forms, can be generalized to describe not only spins of spinors but also spins of vectors as well as spins and charges of scalars, vectors and spinors. If the space (ordinary and noncommutative) has 14 dimensions or more, the appropriate spontaneous break of symmetry leads gravity in $d$ dimensions to manifest in four dimensional subspace as ordinary gravity and all needed gauge fields as well as the Yukawa couplings. Both approaches, the Kähler's one (if generalized) and our, manifest four generations of massless fermions, which are left handed SU(2) doublets and right handed SU(2) singlets. In this talk a possible way of spontaneously broken symmetries is pointed out on the level of canonical momentum.

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arXiv1999

Dirac Relation and Renormalization Group Equations for Electric and Magnetic Fine Structure Constants

The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants - electric $α$ and magnetic $\tilde α$ - were obtained. It was shown that the Dirac relation is valid for the renormalized $α$ and $\tilde α$ at the arbitrary scale, but these RG equations can be considered perturbatively only in the small region: $0.25 \stackrel{<}{\sim} α, \tilde α\stackrel{<}{\sim} 1$ with $\tilde α$ given by the Dirac relation: $α{\tilde α}$ = 1/4.

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arXiv1999

Dirac-Kähler approach connected to quantum mechanics in Grassmann space

We compare the way one of us got spinors out of fields, which are a priori antisymmetric tensor fields, to the Dirac-Kähler rewriting. Since using our Grassmann formulation is simple it may be useful in describing the Dirac-Kähler formulation of spinors and in generalizing it to vector internal degrees of freedom and to charges. The ``cheat'' concerning the Lorentz transformations for spinors is the same in both cases and is put clearly forward in the Grassmann formulation. Also the generalizations are clearly pointed out. The discrete symmetries are discussed, in particular the appearance of two kinds of the time-reversal operators as well as the unavoidability of four families.

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arXiv1999

Phase Transition Couplings in the Higgsed Monopole Model

Using a one-loop approximation for the effective potential in the Higgs model of electrodynamics for a charged scalar field, we argue for the existence of a triple point for the renormalized (running) values of the selfinteraction $λ$ and the "charge" g given by $(λ_{run}, g^2) = (-{10/9} π^2,{4/3}\sqrt{5/3}{π^2}) \approx(-11, 17)$. Considering the beta-function as a typical quantity we estimate that the one-loop approximation is valid with accuracy of deviations not more than 30% in the region of the parameters: $0.2 \stackrel{<}{\sim}{\large α, \tildeα} \stackrel{<}{\sim}1.35.$ The phase diagram given in the present paper corresponds to the above-mentioned region of $α, \tilde α$. Under the point of view that the Higgs particle is a monopole with a magnetic charge g, the obtained electric fine structure constant turns out to be $α_{crit}\approx{0.18_5}$ by the Dirac relation. This value is very close to the $α_{crit}^{lat}\approx{0.20}$ which in a U(1) lattice gauge theory corresponds to the phase transition between the "Coulomb" and confinement phases. Such a result is very encouraging for the idea of an approximate "universality" (regularization independence) of gauge couplings at the phase transition point. This idea was suggested by the authors in their earlier papers.

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arXiv1999

Why do we have parity violation?

We discuss here two of the questions posed at the beginning of the Bled 1998 workshop: Why is the weak charge dependent on handedness? Why do we have parity violation in the Standard Model? It is argued that the quarks and leptons must be protected from gaining a fundamental mass, very large compared to the electroweak scale, by gauge invariance and hence that their gauge charges must depend on handedness. Furthermore we argue that it is the conservation of parity in the electromagnetic and strong interactions rather than parity violation in the weak interactions that needs an explanation. We derive this parity conservation and indeed the whole system of Weyl fermion representations in the Standard Model from a few simple assumptions: Mass protection, small representations, anomaly cancellation and the Standard Model gauge group $S(U(2)\times U(3))$.

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arXiv1999

Masses and mixing angles and going beyond the Standard Model

The idea, following Michel and O'Raifeartaigh, of assigning meaning to the (gauge) \underline{group} and not only the Lie algebra for a Yang Mills theory is reviewed. Hints from the group and the fermion spectrum of the Standard Model are used to suggest the putting forward of our AGUT-model, which gives a very good fit to the orders of magnitudes of the quark and lepton masses and the mixing angles including the CP-breaking phase. But for neutrino oscillations modifications of the model are needed. Baryogenesis is not in conflict with the model.

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arXiv1999

Lattice Chern-Simons Gravity via Ponzano-Regge Model

We propose a lattice version of Chern-Simons gravity and show that the partition function coincides with Ponzano-Regge model and the action leads to the Chern-Simons gravity in the continuum limit. The action is explicitly constructed by lattice dreibein and spin connection and is shown to be invariant under lattice local Lorentz transformation and gauge diffeomorphism. The action includes the constraint which can be interpreted as a gauge fixing condition of the lattice gauge diffeomorphism.

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