arXiv subjects

Renato Nobili

Publications and source records attributed to Renato Nobili.

5 recordsLinked to original sources

arXiv2020

Conformal General Relativity -- Unified Theory of the Standard Models of Elementary Particles and Modern Cosmology

This work may be defined as a modern philosophical approach to theoretical physics. Since ancient times science and philosophy evolved in parallel, thus renewing from time to time the epochal paradigms of human thought. We could not understand how the scientists of the past could have achieved so many goals, if we neglect the philosophical ideas that inspired their minds. Today, despite the spectacular successes of the Standard Models of Elementary Particles (SMEP) and Modern Cosmology (SMMC), theoretical physics seems to be run into a mess of contradictions that preclude the access to higher views. We are still unable to explain why it is so difficult to include gravitation into the SMEP, although General Relativity (GR) works so well in the SMMC, why it is so difficult to get rid of all the divergences of the SMEP, and "why there is something rather than nothing". This paper aims to answer these and other questions by starting from a novel fundamental principle: the spontaneous breaking of conformal symmetry down to the metric symmetry of GR. This statement is very simple but its implementation is a little bit complicated. To facilitate the reading, the paper is divided in a main sequence of sections and subsections and a collection of Appendices. The first acting as a sort of Ariadne's wire for guiding the reader through the labyrinth of specialized topics that are necessary to understand the work.

physics.gen-ph↗

arXiv2016

The Conformal Universe I: Physical and Mathematical Basis of Conformal General Relativity

This is the first of three papers on Conformal General Relativity (CGR), which differs from Einstein's General Relativity (GR) in that it requires action--integral invariance under local scale transformations in addition to general coordinate transformations. The theory is here introduced in the semiclassical approximation as a preliminary approach to a quantum theoretical implementation. The idea of a conformal--invariant extension of GR was introduced by Weyl in 1919. For several decades it had little impact, as CGR implies that all fields are massless. Today this does not appear to be an unsurmountable difficulty since nonzero mass parameters may result from the spontaneous breakdown of conformal symmetry. The theory leads to very interesting results and predictions: 1) the spontaneous breakdown of conformal symmetry is only possible in a 4D--spacetime with small negative curvature; 2) CGR requires the introduction of a ghost scalar field $σ(x)$ invested with geometric meaning and a physical scalar field $φ(x)$ of zero mass, both of which have nonzero vacuum expectation values; 3) in order to preserve $S$--matrix unitarity, $σ(x)$ and $φ(x)$ must interact in such a way that the total energy density is bounded from below; 4) this interaction makes $φ(x)$ behave like a Higgs field of varying mass, which is capable of promoting a huge energy transfer from geometry to matter identifiable as the big bang; 5) in the course of time, the Higgs boson mass becomes a constant and CGR converges to GR.

hep-th↗

arXiv2016

The Conformal Universe III: Basic Mechanisms of Matter Generation

This is the last of three papers on Conformal General Relativity (CGR), which ascribes inflation to a spontaneous breakdown of conformal symmetry, followed by a sudden energy transfer from geometry to matter identified as big bang. This process is driven by a conformal-invariant, unitarity-preserving interaction of two Nambu-Goldstone fields: a ghost scalar field $σ$, invested with geometric meaning, and a physical scalar field $φ$ behaving like a Higgs field of varying mass. The big bang generates a bulk of Higgs bosons at temperature $T_B\simeq 141$ GeV, after which the universe evolves adiabatically while the Higgs bosons decay into Standard-Model particles and the magnitude of the gravitational coupling constant decreases. The process ends when the $σ$-$φ$ interaction potential vanishes, the amplitudes of these fields converge to their expectation values in a final stable vacuum and the Higgs-boson mass converges to about 126 GeV. The main aspects of this phenomenology are qualitatively described and accurately exemplified by numerical simulations. The combination of CGR gravitational equation at time zero with entropy conservation equation results in striking predictions. The best fit to astronomic data is obtained from only standard Higgs boson parameters and a universe age of 19.5 Gyr. The cosmological constant $Λ\simeq 1.35\times 10^{-35}$s$^{-2}$, the scale factor across inflation $Z\simeq 4.54\times 10^{27}$, and the lower bound of the power spectrum of cosmic background anisotropies $W_{min}\!\simeq 37.5\,μ$K$^2$ are thus predicted.

hep-th↗

arXiv2016

The Conformal Universe II: Conformal Symmetry, its Spontaneous Breakdown and Higgs Fields in Conformally Flat Spacetime

This is the second of three papers on Conformal General Relativity (CGR). The conformal group is introduced here as the invariance group of the partial order of causal events in $n$D spacetime. Its general structure, discrete symmetries and field representations are described in detail. The spontaneous breakdown of conformal symmetry is then discussed and the role played by a ghost scalar field and a physical scalar field in 4D spacetime are evidenced. Kinematic--, conformal-- and proper--time hyperbolic coordinates are introduced in a negatively curved Milne spacetime for the purpose of providing three different but equivalent representations of CGR. The first of these is grounded in a Riemannian manifold and is manifestly conformal invariant, the second is grounded in a conformally connected Cartan manifold but its conformal invariance is hidden, the third is grounded in the Riemannian manifold of the Milne spacetime and has the formal structure of General Relativity (GR). The relation between CGR and standard inflationary cosmology is also briefly discussed. Lastly, in view of the detailed study of Higgs--field dynamics carried out in the third paper, the action integrals, motion equations and total energy--momentum tensors of the Higgs field interacting with the dilation field are described in the three representations mentioned above.

hep-th↗

arXiv2008

On von Neumann's Examples of Types

The paper introduces in a new although maybe unusual form the examples of types provided by J. von Neumann and F.J. Murray in their outstanding papers on algebraic factorization (1936-1943)pursuing three main aims: speculating about the physical reasons and motivations that are likely to have been at the origin of von Neumann's investigation; describing the examples of factors provided by those authors with the purpose of clarifying the general concepts standing at the base of the classification of factors into three general types; outlining the perspective of extending the theory to non--separable Hilbert spaces with the purpose of suggesting a novel approach to the representation of infinite systems controlled by external gauge fields.

math-ph↗