arXiv subjects

Robert Delbourgo

Publications and source records attributed to Robert Delbourgo.

14 recordsLinked to original sources

arXiv2016

Grassmann Duality and the Particle Spectrum

Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing sensible Lagrangians anyhow. We apply duality to all of the subgroups within the {\em classification} group SU(3)$\times$SU(2)$_L\times$SU(2)$_R$, which encompasses the standard model gauge group, and thereby determine the full state inventory; this includes the definite prediction of quarks with charge -4/3 and other exotic states. Assuming universal gravitational coupling to the gauge fields and parity even property curvature, we also obtain $4\sin^2θ_w = 1 - 2α/3α_s$ which is not far from the experimental value around the $M_Z$ mass.

hep-th↗

arXiv2016

The Force and Gravity of Events

Local events are characterized by "where", "when" and "what". Just as (bosonic) spacetime forms the backdrop for location and time, (fermionic) property space can serve as the backdrop for the attributes of a system. With such a scenario I shall describe a scheme that is capable of unifying gravitation and the other forces of nature. The generalized metric contains the curvature of spacetime and property separately, with the gauge fields linking the bosonic and fermionic arenas. The super-Ricci scalar can then automatically yield the spacetime Lagrangian of gravitation and the standard model (plus a cosmological constant) upon integration over property coordinates.

hep-th↗

arXiv2016

General Relativity for N Properties

We determine the coefficients of the terms multiplying the gauge fields, gravitational field and cosmological term in a scheme whereby properties are characterized by $N$ anticommuting scalar Grassmann variables. We do this for general $N$, using analytical methods; this obviates the need for our algebraic computing package which can become quite unwieldy as $N$ is increased.

hep-th↗

arXiv2016

The relativity of Colour

By attaching three anticommuting Lorentz scalar (colour) property coordinates to space-time, with an appropriate extended metric, we unify gravity with chromodynamics: gauge transformations then just correspond to coordinate transformations in the enlarged spacetime-property space.

hep-th↗

arXiv2015

The Relativity of Chiral Property

The standard model ascribes distinct properties to different chiralities of fermions. We show how to incorporate this aspect in an extended spacetime-property framework involving two different attributes using a generalized metric which includes gauge fields as well as gravitation. Because the gauge fields are accompanied by coupling constants, all such schemes, including ours, necessitate coupling unification at high energy to ensure universality of gravitational interactions with matter.

hep-th↗

arXiv2014

Where-When-What: the general relativity of space-time-property

We develop the general relativity of extended spacetime-property for describing events including their properties. The anticommuting nature of property coordinates, augmenting space-time $({\bf x},t)$, allows for the natural emergence of generations and for the simple incorporation of gauge fields in the spacetime-property sector. With one electric property this results in a geometrical unification of gravity and electromagnetism, leading to a Maxwell-Einstein Lagrangian plus a cosmological term. Addition of one neutrinic and three chromic properties should lead to unification of gravity with electroweak and strong interactions.

hep-th↗

arXiv2013

The relativity of space-time-property

We describe a geometrical way to unify gravity with the other natural forces by adding fermionic Lorentz scalar variables, characterising attribute, or property, to space-time location. [With five such properties one can accommodate all known leptons and quarks.] Using just one property, viz. electricity, the general relativity of such a scheme and its superscalar curvature automatically produces the Einstein-Maxwell Lagrangian and a cosmological term. By adding more properties we envisage the geometrical unification of the standard model with gravitation.

hep-ph↗

arXiv2013

The Quark-Level Linear σ Model

This review of the quark-level linear σmodel is based upon the dynamical realization of the pseudoscalar and scalar mesons as a linear representation of SU(2) x SU(2) chiral symmetry, with the symmetry weakly broken by current quark masses. In its simplest SU(2) incarnation, with two non-strange quark flavors and three colors, this nonperturbative theory, which can be selfconsistently bootstrapped in loop order, is shown to accurately reproduce a host of low-energy observables with only one parameter, namely the pion decay constant f_π. Extending the scheme to SU(3) by including the strange quark, equally good results are obtained for many strong, electromagnetic, and weak processes just with two extra constants, viz. f_K and $\langleπ|H_{\mbox{\scriptsize weak}}|K\rangle$. Links are made with the vector-meson-dominance model, the BCS theory of superconductivity, and chiral-symmetry restoration at high temperature. Finally, these ideas are cautiously generalized to the electroweak sector, including the W, Z, and Higgs bosons, and also to CP violation.

hep-ph↗

arXiv2012

Properties, Generations and Masses

Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles very naturally. In contrast to the standard model, where masses arise through independent Yukawa couplings to a single Higgs isodoublet, property models produce Higgs fields in various multiplet denominations, but contain a single Yukawa coupling. A renormalizable superHiggs potential of quartic order then produces very strongly constrained masses for generations of fields, which depend on just three constants. By allowing for a small parameter, which is meant to characterise the quantum loop effects for the effective potential, one can obtain nonzero masses for the engendered masses. We illustrate the phenomenon for two and three complex coordinates; the more realistic case of five complex coordinates is not yet fully treatable because of its complexity.

hep-ph↗

arXiv2011

On 2D Periodic Hexagonal Cells

Graphene, the new wondrous material, is a perfect example of a two-dimensional hexagonal crystal unlike any other. Here we exhibit some of the characteristic directional features associated with hexagonal cells, emphasising the sixfold symmetry. We depict the X-ray, vibrational and electronic band structures to be expected in such systems via 2 dimensional contour plots.

cond-mat.mtrl-sci↗

arXiv2009

Inverse momentum expectation values for hydrogenic systems

By using the Fourier transforms of the general hydrogenic bound state wave functions (as ultraspherical polynomials) one may find expectation values of arbitrary functions of momentum p. In this manner the effect of a reciprocity perturbation 1/p can be evaluated for all hydrogenic states.

math-ph↗

arXiv2007

Born reciprocity and the 1/r potential

Many structures in nature are invariant under the transformation (p,r)->(br,-p/b), where b is some scale factor. Born's reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We investigate this idea for atomic physics and galactic motion, where one is basically dealing with a 1/r potential and the observations are very accurate, so as to determine the scale $b = mΩ$. We find that an $Ω\sim 1.5\times 10^{-15}$ Hz has essentially no effect on atomic physics but might possibly offer an explanation for galactic rotation, without invoking dark matter.

hep-th↗

arXiv2006

Flavour mixing and mass matrices via anticommuting properties

Five anticommuting property coordinates can accommodate all the known fundamental particles in their three generations plus more. We describe the points of difference between this scheme and the standard model and show how flavour mixing arises through a set of expectation values carried by a single Higgs superfield.

hep-th↗

arXiv2006

The Flavour of Gravity

By attaching five (complex) anticommuting property coordinates to the four (real) commuting space-time ones, it is possible to accommodate all the known fundamental particles in their three generations. A general relativistic extension to space-time-property can be carried out such that the gauge fields find their place in the space-property sector and the Higgs scalars in the property-property sector. The full curvature is the sum of the gravitational curvature, the gauge field Lagrangian and the Higgs field contribution; property curvature may be linked to the cosmological term.

hep-th↗