Yuval Ne'eman

Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance

In Einsteins gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group A(4, R) and of its subgroup GL(4, R) in four dimensions, energy-momentum and hypermomentum currents of matter are canonically coupled to the coframe and to the connection of a metric-affine spacetime with nonvanishing torsion and nonmetricity, respectively. Fermionic matter can be described in this framework by half-integer representations of the SL(4, R) covering subgroup. We set up a (first-order) Lagrangian formalism and build up the corresponding Noether machinery. For an arbitrary gauge Lagrangian, the three gauge field equations come out in a suggestive Yang-Mills like form. The conservation-type differential identities for energy-momentum and hypermomentum and the corresponding complexes and superpotentials are derived. Limiting cases such as the Einstein-Cartan theory are discussed. In particular we show, how the A(4, R) may “break down” to the Poincare (inhomogeneous Lorentz) group. In this context, we present explicit models for a symmetry breakdown in the cases of the Weyl (or homothetic) group, the SL(4, R), or the GL(4, R).

Gravity and supergravity as gauge theories on a group manifold

Abstract We construct generalizations of gravity, including supergravity, by writing the theory on the group manifold (Poincare for gravity, the graded-Poincare group for supergravity). The action involves forms over the group, restricted to a 4-dimensional submanifold. The equations of motion produce a Lorentz gauge in gravity and supergravity, and an additional anholonomic supersymmetric coordinate transformation which reduces to the “local supersymmetry” of supergravity.

Irreducible gauge theory of a consolidated Salam-Weinberg model

Abstract We derive the Salam-Weinberg model by gauging an internal simple supergroup SU ( 2 1 ) . The theory uniquely assigns the correct SU(2)L ⊗ U(1) eigenvalues for all leptons, fixes θW = 30°, generates the W±σ, Z0σ and Aσ together with the Higgs-Goldstone I L = 1 2 scalar multiplets as gauge fields, and imposes the standard spontaneous breakdown of SU(2)L ⊗ U(1). The masses of intermediate bosons and fermions are directly generated by SU ( 2 1 ) universality, which also fixes the Higgs field coupling.

Primitive particle model

Abstract The present pattern of six almost identical SU(2)L × U(1) quark or lepton doublet-singlet sets appears to indicate that all matter is “made” of one fundamental fermion set (α0, α−)L, αR0, αR− and two bosons φ B 2 3 and φs0 (in addition to the SU(2)L × U(1) and QCD gauge fields).

Extended Geometric Supergravity on Group Manifolds with Spontaneous Fibration

We review and develop geometrical gauging involving the sequence: Lie group/Principal Bundle, for an Internal symmetry group/Soft Group Manifold, for Non-Internal groups. In the Internal case, we rederive the Ghost-fields and the BRS transformations and equations geometrically. In the case of a Soft Group Manifold, we study Spontaneous Fibration, rederive Gravity and Supergravity and then present Extended geometric Supergravity theories.

Renormalization of Gauge Affine Gravity

Abstract We outline a proof of the renormalizability of a non-riemannian model, based on gauging GL(4, R ), in which Einsteins gravity dominates the low-energy region through a Goldstone-Higgs spontaneous symmetry breakdown mechanism. Whereas in other models of gravity, renormalizability, when proved, is the result of 1 p 4 unitarity-violating propagators, in the present case it follows instead from the Yang-Mills-like features of the theory.

Anomaly-free sequential superunification

Abstract The supergroup SU ( 7 1 ) defines a model with 8 generations of quarks and leptons. One half of these are chiral-inverted. The model represents an anomaly-free SU ( 7 1 ) × U (1) gauge unification theory (GUT).

BRST transformations for an affine gauge model of gravity with local GL(4, R) symmetry

Abstract BRST transformations are constructed for the fields in an affine gauge model of gravity with spontaneously broken local GL (4, R ) symmetry, as a step in the quantization procedure. The invariance of the quantum action under these transformations holds under general gauge fixing conditions.

Internal supergroup prediction for the Goldstone-Higgs particle mass☆

Abstract Using a seemingly ad hoc but phenomenologically fitting global internal supersymmetry SU( 2 1 ) ⊃ SU(2) × U(1) constraining the weak-electromagnetic otherwise arbitrary parameters, we predict for the Goldstone-Higgs particle a mass mH = 2mW, or 160–170 GeV.

The problems in quantum foundations in the light of gauge theories

We review the issues of nonseparability and seemingly acausal propagation of information in EPR, as displayed by experiments and the failure of Bells inequalities. We show that global effects are in the very nature of the geometric structure of modern physical theories, occurring even at the classical level. The Aharonov-Bohm effect, magnetic monopoles, instantons, etc. result from the topology and homotopy features of the fiber bundle manifolds of gauge theories. The conservation of probabilities, a supposedly highly quantum effect, is also achieved through global geometry equations. The EPR observables all fit in such geometries, and space-time is a truncated representation and is not the correct arena for their understanding. Relativistic quantum field theory represents the global action of the measurement operators as the zero-momentum (and therefore spatially infinitely spread) limit of their wave functions (form factors). We also analyze the collapse of the state vector as a case of spontaneous symmetry breakdown in the apparatus-observed state interaction.