Yuval Ne’eman

Unification Through a Supergroup

The representations of supergroups provide the most precise fit to the known set of fundamental physical matter fields. SU(2/1) describes the unified weak electromagnetic interactions and SU(5 + k/1) contains SU(3)colour and 2k exact “generations”. Moreover, SU(2/1) predicts that the fourth states of the lepton multiplets (i.e., υ R O ) decouple, whereas they do not in quark multiplets, and SU(n/l) predicts that the colour degree of freedom is SU(3). We provide all relevant constructions.

A Parallelism Between Quantum Gravity and the IR Limit in QCD (Emergence of Hadron and Nuclear Symmetries)

In the non-perturbative IR region, the action of QCD contains a long-range component, acting as an effective “strong gravity”. It is generated by the exchange of a color neutral pair of gluons \( {G_{{\mu \nu }}}(x) \sim {\eta_{{ab}}}B_{\mu }^{\alpha }(x)B_{\nu }^b(x) \) The G μν acts formally as a Riemannian metric with J P = O +, 2+ quanta coupled symmetrically to nuclear matter and generating the IBM paradigm, Regge trajectories and the string-like features of hadrons.

The superconnection, a different local supersymmetry mode

Abstract After an introduction relating to the late Dennis Sciama, I review the interlocked quantization programs of Gravity and Weyl Yang-Mills gauge theory, including the independent emergence of two superalgebraic systems: (a) Supersymmetry with supermultiplets relating multiplets of different Quantum Statistics: (b) superalgebraic extensions of the calculus of differential forms. The latter include the BRST unitarity-inducing constrains and a new tool, the Quillen Superconnection, with contributions from noncommutative geometry. Two examples are reviewed, one predicting the mass of the Higgs meson in Electroweak theory and the other relating to Riemannian Gravity emerging through a similar mechanism.

Inflationary Cosmogony, Copernican Relevelling and Extended Reality

“Eternal” Inflation has relevelled the creation of universes, making it a “routine” physical occurence. The mechanism of the Big Bang, from the conditions triggering it, to the eventual creation of the entire matter content of the resulting universe, involves no singular physical processes. However, causal horizons, due to General Relativity, separate the newborn universe from the parent universe in which it was seeded as a localized vacuum energy. The new universe’s expansion only occurs “after” infinite time, i.e. “never”, in the parents frame. This forces a reassessment of “reality”. The two universes are connected by the world line of the initial localized vacuum energy, originating in the parent universe. Assuming that the parent universe itself was generated in a similar fashion, etc., an infinite sequence of previous universes is thus connected by one world-line, like a string of beads.

Inflation, the Top and All that

Inflationary Cosmogony was suggested by Alan Guth in 1981 [1], as a solution to an apparent clash between two “Standard Models” — the 1974 SM of the Physics of Particles and Fields and Big Bang Cosmogony (BBC), as the latter theory had crystalized, after the 1965 discovery of the 3K Cosmological Background Radiation (CBR). As a matter of fact, there were already several paradoxes present within BBC itself, difficulties which were known as the Causality (or Homogeneity) and Fine-Tuning (or Flatness) issues. After 1975, the application of the SM new physics added a new paradox, that of the missing Domains and the related issue of the absence of Magnetic Monopoles. In lecture I, we review the basic cosmological formalism; we then discuss the emergence of causal “Horizons” (leading to the Causality Paradox). This is followed by an exposition of the Fine-Tuning issue. Lecture II describes the essentials of the SM of Particle Physics (including a diversion related to the recent discovery of the Top quark), emphasizing the mechanism of Spontaneous Symmetry Breakdown (SSB), which plays an important role, both in causing the apparent clash with cosmological observations and in the subsequent resolution of the difficulty, through the mechanism of Inflation. We discuss the mystery of the missing Domains and Monopoles.

QCD Foundations for Hadron Regge Trajectories and for the Arima-Iachello Symmetries of Nuclei

We review our Pseudo-Gravity hypothesis which points to the two (or more) gluon exchange in QCD as the origin of Regge excitations and a variety of other hadronic features resembling gravity. We present a detailed dynamical study. One effect in nuclei is the emergence of the Arima-Iachello model, with its 2+, 0+ ground state. We explain the relevant dynamics.

Neo-Darwinian Processes in the Evolution of Science and of Human Societies

Determinism dominated the early Nineteenth Century as a central paradigm. Laplace assumed that given the positions and momenta at a given instant for all the particles in the universe, plus extensive computing capabilities (nowadays we would say “given a Cray supercomputer”.) one could reconstruct the entire past and predict the future of the physical world. A contemporary interest in precisely such a problem is provided by meteorology: Given all data about temperature, pressure, wind velocity, cloud coverage (including the heights, i.e. a 4-dimensional problem), earth topographies etc. all over the world, predict tomorrow’s weather (or next month’s). However, atmospheric scientists who work on this problem at the end of the XXth Century know that some questions cannot be answered, due to so-called “chaotic” behavior. As a matter of fact, “chaos” was first identified by E.N. Lorenz in this area.

Universal SU(2/1) and the Higgs and Fermion Masses

We review the SU(2/1) internal supersymmetry suggested by D. Fairlie and the author in 1979. The initial apparent difficulties were resolved when, with J. Thierry-Mieg, we understood that the gauging of a supergroup implies taking the usual Yang-Mills-like Principal (Double) Fibre Bundle as a “scaffold” and using its Grassmann algebra as parameter manifold for the supergauge. SU(2/1) Universality fixes the masses of the Higgs scalar field and the “top” quark around 100–200 GeV, in the same region as the W and Z masses. A “unified” supergauge, enclosing SU(3)colour × SU(2) x U(1), predicts a fourth lepton generation in which the neutrino mass is of the same order.

Towards a Renormalizable Theory of Quantum Gravity

The difficulties in quantizing gravity are due to the non-Lie-algebra nature of the gauged translation operators and to the dimensional nature of the Newton constant. The first issue may be dealt with by gauging the infinite Lie algebra of the diffeomorphisms. The second is solved if gravity is represented by a gl (4,R) gauge with dimensionless coupling, with Einstein’s theory and Newton’s coupling resulting from spontaneous symmetry breakdown (i.e. a low energy effective theory).

Superalgebras, Supergroups and Geometric Gauging

This lecture series falls into two parts: I. Superalgebras, Supergroups and Supermanifolds. This is mathematical in its content, but the presentation is for physicists. The applications of the “supers” have been in the forefront in recent years, and most mathematical texts do not contain the necessary material - simply because the mathematical content is also extremely recent. II. Forms on a (Rigid) Group Manifold, a Principal Bundle and a Soft (Dali) Group Manifold. We develop the elements of the exterior calculus, on a Lie Group Manifold, thus reproducing results going back to Cartan etc. We then develop the geometric theory of gauging. For a local internal symmetry, this is done on a Principal Bundle. For a non-internal group such as the Poincare or Super Poincare groups, we reproduce Gravity and Supergravity by using a “soft” Group Manifold, i.e. a manifold whose tangent is the original rigid group. We construct the relevant theory, which we have recently developed in collaboration with T. Regge and J. Thierry-Mieg.