arXiv subjects

R. K. Nesbet

Publications and source records attributed to R. K. Nesbet.

18 recordsLinked to original sources

arXiv2023

Conformal theory of gravitation and cosmic expansion

The postulate of universal Weyl conformal symmetry for all elementary physical fields introduces nonclassical gravitational effects in both conformal gravitation(CG) and the conformal Higgs model (CHM). The resulting theory is found to explain major observed phenomena including excessive galactic rotation velocities and accelerating Hubble expansion, without invoking dark matter (DM). The recent history of this development is surveyed here. Implications of the theory include galactic baryonic Tully-Fisher relations and dark galactic haloes of definite large radius. Cosmological CHM parameters exclude a massive Higgs boson but are consistent with a novel alternative particle of the observed mass.

gr-qc↗

arXiv2022

Conformal gravity: Newton's constant is not universal

Newton's gravitational constant $G$ has been measured to high accuracy in a number of independent experiments. For currently unresolved reasons, indicated values from different well-designed and thoroughly analyzed experiments differ by more than the sum of estimated errors. It has recently been shown that requiring both Einstein general relativity and the Higgs scalar field model to satisfy conformal symmetry (local Weyl scaling covariance) introduces gravitational effects that explain anomalous galactic rotation, currently accelerating Hubble expansion, and dark galactic halos, without invoking dark matter. This implies different values $G_n$ and $G_p$ for neutron and proton, respectively, but retains the Einstein equivalence principle for test objects accelerated by a given gravitational field. Isotopic mass defect $μ$ per nucleon determines independent $G_m$. Thus G differs for each nuclear isotope. Several recent measurements are used here to estimate $G_n=6.60216$, $G_p=6.38926$, and $G_m=-11.60684$ in units $10^{-11}m^3kg^{-1}s^{-2}$.

physics.gen-ph↗

arXiv2022

Weyl conformal symmetry model of the dark galactic halo

The postulate of universal conformal (local Weyl scaling) symmetry modifies both general relativity and the Higgs scalar field model. The conformal Higgs model (CHM) generates an effective cosmological constant that fits observed accelerating Hubble expansion for redshifts $z\leq 1$ (7.33 Gyr) accurately with only one free parameter. Growth of a galaxy is modeled by central accumulation of matter from an enclosing empty spherical halo whose radius expands with depletion. Details of this process account for the nonclassical radial centripetal acceleration observed as excessive orbital velocities in galactic haloes. There is no need for dark matter.

gr-qc↗

arXiv2022

Implications of the conformal Higgs model

The postulate of universal local Weyl scaling (conformal) symmetry modifies both general relativity and the Higgs scalar field model. The conformal Higgs model (CHM) acquires a cosmological effect that fits observed accelerating Hubble expansion for redshifts $z\leq 1$ (7.33 Gyr) accurately with only one free constant parameter. Conformal gravity (CG) has recently been fitted to anomalous rotation data for 138 galaxies. Conformal theory explains dark energy and does not require dark matter, providing a viable alternative to the $Λ$CDM standard paradigm. The theory precludes a massive Higgs particle but validates a composite gauge field $W_2$ with mass 125GeV.

gr-qc↗

arXiv2021

Conformal Higgs model: Gauge fields can produce a 125GeV resonance

Recent cosmological observations and compatible theory offer an understanding of long-mysterious dark matter and dark energy. The postulate of universal conformal local Weyl scaling symmetry, without dark matter, modifies action integrals for both Einstein-Hilbert gravitation and the Higgs scalar field by nonclassical gravitational terms. Conformal theory accounts both for observed excessive external galactic orbital velocities and for accelerating cosmic expansion. SU(2) symmetry-breaking is retained but dark energy is implied rather than nonzero Higgs particle mass. These results are compatible with existence of a massive neutral particle or resonance $W_2$ at 125GeV, described as composite scalar $g_{μν}W_-^μW_+^ν$ and $g_{μν}Z^{μ*}Z^ν$ interacting strongly via quark exchange. Decay modes would be consistent with those observed at LHC. Higgs scalar field $Φ$ is dressed by the $W_2$ field to produce Lagrangian term $λ(Φ^\daggerΦ)^2$.

physics.gen-ph↗

arXiv2020

Conformal theory of gravitation and cosmology

The postulate of universal local Weyl scaling (conformal) symmetry modifies both general relativity and the Higgs scalar field model. Conformal gravity (CG) has recently been fitted to rotation data for 138 galaxies. The conformal Higgs model (CHM) acquires a gravitational effect that fits observed Hubble expansion for redshifts $z\leq 1$ (7.33 Gyr) accurately with only one free constant parameter. The astrophysical data fitted by these two conformal models is shown here to account for both arbitrary parameters $w^2$ and $λ$ of postulated Higgs potential $V=-(w^2-λΦ^\daggerΦ)Φ^\daggerΦ$, responsible for symmetry-breaking finite $Φ^\daggerΦ$ in electroweak particle theory. The present analysis resolves recent criticism of CG. CG and CHM are shown here to be interdependent but compatible. Nonclassical CG acceleration $γ$ is shown to be determined by the CHM. Conformal theory explains dark energy and does not require dark matter, a viable alternative to the $Λ$CDM standard model. A recently established empirical relationship between classical and nonclassical galactic radial acceleration requires parameter $γ$ to be independent of galactic mass. Conformal theory is shown here to be consistent with this and with the $v^4$ baryonic Tully-Fisher relation for galactic rotation velocities. Vanishing of centripetal acceleration outside a halo boundary is a unique implication of the theory.

physics.gen-ph↗

arXiv2019

Dark energy density predicted and explained

It has recently been shown that the observed Hubble function for cosmological expansion can be fitted accurately back to redshift unity (7.33 Gyr ago) with only one free constant, while neglecting cosmic curvature and mass, using the modified Friedmann equation implied by subjecting the Higgs scalar field model to conformal Weyl scaling symmetry. Time-dependent solutions of the relativistic conformal Higgs scalar field equation coupled with the conformal Friedmann equation are shown here to imply dark energy of the observed magnitude. Predicted persistent cosmic acceleration is consistent with the nonclassical parameter inferred by conformal theory from observed excessive galactic rotation velocities and galactic dark halos, all without dark matter.

physics.gen-ph↗

arXiv2018

Theoretical implications of the galactic radial acceleration relation of McGaugh, Lelli, and Schombert

Velocities in stable circular orbits about galaxies, a measure of centripetal gravitation, exceed the expected Kepler/Newton velocity as orbital radius increases. Standard LCDM attributes this anomaly to galactic dark matter. McGaugh et al have recently shown for 153 disc galaxies that observed radial acceleration is an apparently universal function of classical acceleration computed for observed galactic baryonic mass density. This is consistent with the empirical MOND model, not requiring dark matter. It is shown here that suitably constrained LCDM and conformal gravity (CG) also produce such a universal correlation function. LCDM requires a very specific dark matter distribution, while the implied CG nonclassical acceleration must be independent of galactic mass. All three constrained radial acceleration functions agree with the empirical baryonic $v^4$ Tully-Fisher relation. Accurate rotation data in the nominally flat velocity range could distinguish between MOND, LCDM, and conformal gravity.

astro-ph.GA↗

arXiv2015

Dark galactic halos without dark matter

Using standard Einstein theory, baryonic mass cannot account for observed galactic rotation velocities and gravitational lensing, attributed to galactic dark matter halos. In contrast, theory constrained by Weyl conformal scaling symmetry explains observed galactic rotation in the halo region without invoking dark matter. An explanation of dark halos, gravitational lensing, and structural stabilization, without dark matter and consistent with conformal theory, is proposed here. Condensation of uniform primordial matter into a material cloud or galaxy vacates a large surrounding spherical halo. Within such an extended vacancy in the original cosmic background mass-energy density, conformal theory predicts centripetal acceleration of the observed magnitude.

physics.gen-ph↗

arXiv2011

The Higgs scalar field with no massive Higgs particle

The postulate that all massless elementary fields have conformal Weyl local scaling symmetry has remarkable consequences for both cosmology and elementary particle physics. Conformal symmetry couples scalar and gravitational fields. Implications for the scalar field of a conformal Higgs model are considered here. The energy-momentum tensor of a conformal Higgs scalar field determines a cosmological constant. It has recently been shown that this accounts for the observed magnitude of dark energy. The gravitational field equation forces the energy density to be finite, which precludes spontaneous destabilization of the vacuum state. Scalar field fluctuations would define a Higgs tachyon rather than a massive particle, consistent with the ongoing failure to observe such a particle.

physics.gen-ph↗

arXiv2009

Higgs mass determined by cosmological parameters

Postulating that all massless elementary fields have conformal scaling symmetry removes a conflict between gravitational theory and the standard model of elementary quantum fields. If the scalar field essential to SU(2) symmetry breaking has conformal symmetry, it must depend explicitly on the Ricci curvature scalar of gravitational theory. This has profound consequences for both cosmology and elementary particle physics, since cosmological data determine scalar field parameters. A modified Friedmann equation is derived and solved numerically. The theory is consistent with all relevant data for supernovae redshifts below $z=1$. The implied value of the cosmological constant implies extremely small Higgs mass, far below current empirical lower bounds. Detection of a Higgs boson with large mass would falsify this argument.

hep-th↗

arXiv2008

Neutrino and scalar boson mass in algebraic quantum field theory

The hypothesis is explored that fermion rest mass is due entirely to self-interaction via virtual excitation of gauge bosons. This requires revising the standard model to treat both chiral projections of a fermion field as SU(2) doublets, which precludes Yukawa coupling to a scalar (Higgs) boson field. The estimated self-interaction mass of the electron neutrino is $0.291\times10^{-5}m_e$. The implied self-interaction mass of the Higgs boson itself is very small, comparable to the neutrino. Because there is no direct coupling to fermions, only to the $Z^0$ gauge boson, this can be reconciled with failure to detect low-mass Higgs bosons. This argument eliminates many undetermined parameters of the standard model, but requires an {\it ad hoc} Lagrangian term to account for neutral current asymmetries. The proposed algebraic formalism is consistent with fermion generations defined by distinct eigenvalues of a self-interaction mass operator.

hep-th↗

arXiv2006

Self-interaction and mass in quantum field theory

Qualitative implications of electroweak theory are reconsidered on the assumption that the unique source of fermion rest mass is self-interaction via coupling to gauge fields. This implies small but nonzero mass for neutrinos, and suggests that successive fermion generations are distinct coupled-field eigenstates of a self-interaction mass operator. For a scalar Higgs field, this mechanism can account for the SU(2) symmetry breaking of electroweak theory without a biquadratic self-interaction. The implied Higgs particle mass could be very small, eluding any search limited to heavy particles.

hep-ph↗

arXiv2003

Nonlocal potentials in independent-electron models

This note summarizes the motivation for extending current density-functional theory to include nonlocal one-electron potentials, and proposes methodology for practical calculations. The theoretical model, orbital functional theory, has been shown to be exact in principle for the general N-electron problem, but must depend in practice on a parametrized correlation energy functional. The discussion here is intended to honor Lee Allen and to bring up to date some conversations that we began in 1954.

cond-mat↗

arXiv2003

Nonlocal potentials for short-range electronic correlation in atoms, molecules, and solids

Extending density functional theory (DFT) to an {\it ab initio} orbital functional theory (OFT) requires new methodology for nonlocal exchange and correlation potentials. This paper describes such modifications to a standard Dirac-Slater atomic program. Unrestricted Hartree-Fock (UHF) theory is extended by a modified Colle-Salvetti Ansatz for short-range electronic correlation. Results are reported for atoms He-Ne. Values of parameters needed for similar calculations on molecules and solids are reported. Implementation of nonlocal exchange and correlation for such extended systems, using multiple scattering theory to connect independent calculations in space-filling atomic cells, is discussed.

cond-mat↗

arXiv2003

Reply to Comment by Holas and March

The accompanying Comment by A. Holas and N. H. March [Phys. Rev. A {\bf 66}, 066501 (2002)] is concerned with the issue of whether or not kinetic energy can be represented by an effective local potential, as required for an exact Thomas-Fermi theory equivalent to Kohn-Sham density-functional theory. They dispute [R.K. Nesbet, Phys. Rev. A {\bf 65}, 010502(R) (2001)], which concludes that for more than two electrons the use by Kohn and Sham of the Schrödinger kinetic energy operator is variationally correct, while the equivalent local potential required for a valid Thomas-Fermi theory, a Fréchet functional derivative of the Kohn-Sham ground-state kinetic energy functional, does not exist. The argument of Holas and March is clearly invalid for the simple example of the lowest triplet state of a two-electron atom with noninteracting electrons. Why this fails, as do earlier arguments in the literature, has been explained in recent publications, summarized here.

physics.atom-ph↗

arXiv2003

Reply to Lindgren and Salomonson

In the accompanying Comment [Phys. Rev. A {\bf 67}, 056501 (2003)], I. Lindgren and S. Salomonson claim to prove for the Kohn-Sham kinetic energy functional of ground state electron density that a Frëchet functional derivative exists, equivalent to a multiplicative local potential function. If true, this result would imply an exact Thomas-Fermi theory for ground states of noninteracting electrons. However, such a theory is not consistent with the exclusion principle for more than one electron of each spin. The simplest counterexample is the lowest triplet state of a noninteracting two-electron atom. If only the total electron density were normalized, as in Thomas-Fermi theory, the lowest state would collapse into a doubly-occupied $1s$ spin-orbital. Two independent parameters $ε_{1s}$ and $ε_{2s}$ are required to maintain independent subshell normalization. The argument presented by these authors is discussed in the light of this unphysical implication.

physics.atom-ph↗

arXiv2003

Variational derivation of density functional theory

It is shown here that Kohn-Sham equations cannot be derived from Hohenberg-Kohn theory without an additional postulate. Assuming that a functional derivative with respect to total electron density exists leads in general to a theory inconsistent with the exclusion principle. A mathematically and physically correct variational theory of the Kohn-Sham model can be developed using functional derivatives with respect to orbital densities. These partial (Gâteaux) derivatives can be constructed explicitly from general N-electron theory and are defined throughout the orbital Hilbert space. This theory is consistent with the local density approximation (LDA), but does not in general imply multiplicative local exchange-correlation potentials. Progress beyond the LDA in condensed-matter physics requires development of methodology for nonlocal exchange and correlation potentials.

cond-mat↗