Holger Bech Nielsen

Vortex Line Models for Dual Strings

We call attention to the possibility of constructing field theories for the dual string. As an example, we show that a Higgs type of Lagrangian allows for vortex-line solutions, in analogy with the vortex lines in a type II superconductor. These vortex lines can approximately be identified with the Nambu string. In the strong coupling limit we speculate that the vortex lines make up all low energy phenomena. It turns out that this strong coupling limit is “super quantum mechanical” in the sense that the typical action of the theory is very small in comparison with Planks constant.

Hierarchy of Quark Masses, Cabibbo Angles and CP Violation

Some ideas are put forward towards understanding the fact that mass ratios of quarks or leptons are usually rather large. These speculations are based on the assumption that the basic (bare) couplings at small distances are all of the same order of magnitude but otherwise unknown or random. The most promising explanation requires the bare left- and right-handed components of a quark to have different values for some almost conserved quantum number. These differences determine the order of magnitude of the corresponding quark mass. The generalized Cabibbo mixing angle connecting two types of quarks is then predicted to be given order of magnitude wise by the square root of the corresponding quark mass ratio. However, it is difficult to understand why CP is so well conserved.

SCALING OF MULTIPLICITY DISTRIBUTIONS IN HIGH ENERGY HADRON COLLISIONS.

Abstract It is shown that asymptotically 〈 n 〉 σ n ( s ) is only a function of n /〈 n 〉, where σ n ( s ) is the multiplicity distribution. The essential assumption in deriving this result is that multiparticle inclusive cross sections obey the scaling law. It is also pointed out that the available data below 30 GeV may possibly indicate rather long-range correlations in multi-body reactions.

Absence of neutrinos on a lattice: (I). Proof by homotopy theory

Abstract It is shown, by a homotopy theory argument, that for a general class of fermion theories on a Kogut-Susskind lattice an equal number of species (types) of left- and right-handed Weyl particles (neutrinos) necessarily appears in the continuum limit. We thus present a no-go theorem for putting theories of the weak interaction on a lattice. One of the most important consequences of our no-go theorem is that is not possible, in strong interaction models, to solve the notorious species doubling problem of Dirac fermions on a lattice in a chirally invariant way.

ADLER-BELL-JACKIW ANOMALY AND WEYL FERMIONS IN CRYSTAL

The Adler-Bell-Jackiw (ABJ) axial anomaly is derived from the physical point of view as the production of Weyl particles and it is used to show the absence of the net production of particles for lattice regularized chirally invariant theories with locality. An analogy or a simulation is pointed out between the Weyl fermion theory and gapless semiconductors where two energy bands have pointlike degeneracies. For such materials, in the presence of parallel electric and strong magnetic fields, there exists an effect similar to the ABJ anomaly that is the movement of the electrons in the energy-momentum space from the neighborhood of one degeneracy point to another one. The longitudinal magneto-conduction becomes extremely strong.

Absence of neutrinos on a lattice: (II). Intuitive topological proof

Abstract An intuitive topological proof is given of the no-go theorem for putting Weyl fermions in weak interaction on a lattice, or for constructing chiral invariant lattice QCD, which was proved by a homotopy theory argument in our preceding paper (Absence I). This theorem hangs on the existence of the charge (e.g. fermion number), and thus on the complex-field formulation and on locality. If we relax the assumptions for the no-go theorem, for instance the existence of the charge, and thus use the real-field formulation, we can construct a model that has only one two-component field. We can assign this model an only approximately conserved charge.

A no-go theorem for regularizing chiral fermions

Abstract We present a no-go theorem for regularizing chiral fermions in a general and abstract form, together with a review of our lattice no-go theorem for chiral fermions.

Origin of symmetries

The development in our understanding of symmetry principles is reviewed. Many symmetries, such as charge conjugation, parity and strangeness, are no longer considered as fundamental but as natural consequences of a gauge field theory of strong and electromagnetic interactions. Other symmetries arise naturally from physical models in some limiting situation, such as for low energy or low mass. Random dynamics and attempts to explain all symmetries - even Lorentz invariance and gauge invariance - without appealing to any fundamental invariance of the laws of nature are discussed. A selection of original papers is reprinted.

A QUANTUM LIQUID MODEL FOR THE QCD VACUUM Gauge and rotational invariance of domained and quantized homogeneous color fields

We show that domains are formed in a homogeneous SU(2) color magnetic field. Due to quantum fluctuations the domains have fluid properties. It is then argued that, quantum mechanically, superpositions of such domains must be considered. The resulting state is gauge and rotational invariant, in spite of the fact that the original color magnetic field breaks these invariances. We point out that in our model for the QCD vacuum, color magnetic monopoles are not confined.

Standard model criticality prediction top mass 173 ± 5 GeV and Higgs mass 135 ± 9 GeV

Abstract Imposing the constraint that the Standard Model effective Higgs potential should have two degenerate minima (vacua), one of which should be — order of magnitude wise — at the Planck scale, leads to the top mass being 173 ± 5 GeV and the Higgs mass 135 ± 9 GeV. This requirement of the degeneracy of different phases is a special case of what we call the multiple point criticality principle. In the present work we use the Standard Model all the way to the Planck scale, and do not introduce supersymmetry or any extension of the Standard Model gauge group. A possible model to explain the multiple point criticality principle is lack of locality fundamentally.