arXiv subjects

Richard Shurtleff

Publications and source records attributed to Richard Shurtleff.

At least 19 recordsLinked to original sources

arXiv2016

The Lorentz Group with Dual-Translations and the Conformal Group

For those finite-matrix representations of the Lorentz group of rotations/boosts with spin $(A,B)\oplus(C,D)$ that can also represent translations, two possible translation subgroups qualify. Of these two, one must be selected, and one discarded, to represent the Poincar\'{e} group of rotations/boosts with translations in spacetime. Instead, let us discard the requirement that there be just one translation subgroup. With dual-translations, one gives up agreement with simple macroscopic observations of spacetime. Now the transformations of both possible translation subgroups combine with those of the Lorentz group. The resulting commutation relations require new transformations and generators to satisfy the linearity requirement of a Lie algebra. Special cases of spins are sought to restrict the influx of new transformations. One finds that the Dirac 4-spinor formalism is the only viable solution. The slightly expanded group it represents is the conformal group with just one new transformation, scale change. It follows as a corollary that the Dirac 4-spinor formalism is the only matrix representation of the conformal group with spin $(A,B)\oplus(C,D).$

physics.gen-ph↗

arXiv2014

Testing the Alignment Tendency of Some Polarized Radio Sources

Measuring the alignment of polarized radio sources requires comparing vectors at different locations on the sky, i.e. on a sphere. A test of alignment is derived herein. While both large scale and coordinate independent, the test avoids the mathematical subtleties involved when comparing vectors at different locations on a curved surface. Applied to 5442 sources drawn from a published catalog, the analysis finds a level of alignment that would be matched by only 7% to 14% of data sets with the same sources but with random polarization directions. The locations of the sources involved and the directions that the vectors favor and the regions avoided are described as well.

astro-ph.CO↗

arXiv2013

A Large Scale Pattern from Optical Quasar Polarization Vectors

The 355 optically polarized QSOs have redshifts from 0.061 to 3.94 and are spread out over the sky except for a 60 degree band centered on the Galactic Equator. The data we analyze was measured, collected and published by others. Here, we apply tests suitable for large-scale samples and find that the polarization directions align with a significance of p = 1% by one test and are correlated by a second test with p = 5%, each p-value uncertain within a factor of about 2. The tests return a preferred Cartesian coordinate system that fortuitously aligns well with the Milky Way Galaxy with a significance of p = 3%. Thus, the Hub Tests' results combined together imply the polarization directions are correlated with a significance that is much less than 1%, which is remarkable for such a large-scale sample.

astro-ph.CO↗

arXiv2011

Scattering Relativity in Quantum Mechanics

By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.

physics.gen-ph↗

arXiv2011

U(N) Based Transformations in N-Squared Dimensions

Consider the example of the relationship of the group O(3) of rotations in 3-space to the special unitary group SU(2). Given other unitary groups, what transformations can we find? In this paper we describe a method of constructing transformations in an N-squared dimensional manifold based on the properties of the unitary group U(N). With N = 2, the method gives the familiar rotations, boosts, translations and scale transformations of four dimensional spacetime. In the language of spacetime now applied for any N, we show that rotations preserve distances and times. There is a scale-changing transformation. For N more than 2, boosts do not preserve generalized spacetime intervals, but each N-squared dimensional manifold contains a 3+1 dimensional subspace with invariant spacetime intervals. That each manifold has a four dimensional spacetime subspace correlates with the property of U(N) that U(2) is a subgroup.

math-ph↗

arXiv2010

A Spacetime for SU(N)

The rotations, boosts, and translations in an N^2-dimensional spacetime are shown to be related to the fundamental commutators, anticommutators, and Clebsch-Gordan coefficients, respectively, of SU(N).

math-ph↗

arXiv2010

A Spacetime for SU(3)

Rotations, boosts and translations in 8 + 1 spacetime are developed based on the commutation and anticommutation relations of SU(3). The process follows a process that gives 3 + 1 spacetime from SU(2).

math-ph↗

arXiv2010

Spacetime is for SU(2)

The generators of rotations, boosts and translations are built up based on the commutation and anticommutation relations of the fundamental two dimensional representation of SU(2). Rotations in spacetime derive from the commutation relations of SU(2). Boosts derive from the anticommutation relations of SU(2).

math-ph↗

arXiv2009

Ultra-High Energy Cosmic Rays from Galactic Supernovae

Suppose that even the highest energy cosmic rays (CRs) observed on Earth are protons accelerated in local Milky Way Galaxy sources, with few if any from more distant sources. In this paper we treat the problem that supernovae remnants likely produce protons with energies up to about a PeV, but CRs with 100s of EeV energy are observed. We assume with minimal comment the idea that `new physics' is at work and we accept that a CR's collision energy at the Earth exceeds its kinetic energy as it travels through the Galaxy. There is some evidence that the collision energy-kinetic energy difference has been seen at the Tevatron and LHC, but it is small enough to attribute to standard physics. This sets the threshold for energy bifurcation. Based on this threshold and the CR spectrum endpoint, a formula for collision energy as a function of kinetic energy is derived. With the function and the observed CR spectrum we can predict the average spectrum of CR sources. Also we can estimate the collision energies of proton beams as terrestrial particle accelerators advance and produce beams with higher kinetic energies.

astro-ph.HE↗

arXiv2009

Formulas for SU(3) Matrices

Formulas are developed for the eight basis matrices {T^+,T^-,T^3,V^+,V^-,U^+,U^-,U^3} of the finite dimensional (p,q)-irreducible representation of SU(3). Two computer programs, one in an interpretive language and one in a compiled language, are included. Given p and q, each calculates the eight basis matrices.

math-ph↗

arXiv2008

On the Very-High-Energy Gamma Ray Spectra from Typical Supernovae Remnants

Recently measured VHE gamma ray spectra from supernovae remnants (SNRs) are best fit by power laws with an exponential cutoff. But this feature does not occur at the `knee-equivalent' energy at which VHE gamma ray spectra are expected to reflect the `knee' in the otherwise featureless cosmic ray spectrum. In this article, the VHE gamma ray feature is explained as a consequence of a recently deduced quantum effect. The effect distinguishes `trajectory energy' from `particle state energy' and requires that the particle state energy depends strongly on gravitational potential at very high energies. Based on this effect and the observed CR spectrum, a tight two-parameter fit is obtained to the combined VHE gamma ray spectra of SNRs RX J1713.7-3946 and RX J0852.0-4622 and the Galactic Center ridge.

astro-ph↗

arXiv2008

Quantum Fields and Translations

Modifications of a free quantum field calculation using translation-related concepts and general translation representations yield quantum fields for massive particles that as a consequence follow the classical trajectories of electrodynamics and geometrodynamics. The work allows an explanation for the unexpectedly high energy of cosmic rays. The explanation can be tested at the Large Hadron Collider once high energy proton beams are operational.

hep-th↗

arXiv2008

Gravity, Cosmic Rays and the LHC

The high energy proton beams expected when the Large Hadron Collider (LHC) comes online should provide a pass/fail test for a gravity-related explanation of ultrahigh energy cosmic rays. The model predicts that particles have two kinds energies, equal for null gravitational potentials and, in the potential at the Earth, differing significantly above one TeV. If correct, a 7 TeV trajectory energy proton at the LHC would deliver a 23.5 TeV particle state energy in a collision.

hep-ph↗

arXiv2007

Dual Phase Cosmic Rays

A calculation based on flat spacetime symmetries shows how there can be two quantum phases. For one, extreme phase change determines a conventional classical trajectory and four-momentum, i.e. mass times four-velocity. The other phase occurs in an effective particle state, with the effective energy and momentum being the rate of change of the phase with respect to time and distance. A cosmic ray proton moves along a classical trajectory, but exists in an effective particle state with an effective energy that depends on the local gravitational potential. Assumptions are made so that a cosmic ray proton in an ultra-high energy state detected near the Earth was in a much less energetic state in interstellar space. A 300 EeV proton incident on the Earth was a 2 PeV proton in interstellar space. The model predicts such protons are in states with even more energy near the Sun than when near the Earth.

astro-ph↗

arXiv2007

Forcing Free Fields

The momentum of a free massive particle, invariant under translation, thereby realizes a trivial representation of the translation group. By allowing nontrivial reps of translations, momentum changes with translation, a recipe for force. Here the procedure is applied to the conventional construction of a free quantum field using spacetime symmetries, yielding a more general field with the free field as a special case. It is shown that a particle described by the quantum field follows the classical trajectories of a massive charged particle in electromagnetic and gravitational fields.

hep-th↗

arXiv2007

Massive Particle Fields, with Momentum Matrices

It is well known that an essentially unique free massive particle field of given spin can be constructed as a linear combination of the annihilation and creation operators for free single particle states. And the given spin determines the transformation of the field components for rotations and boosts. But the usual construction restricts translations; the components are simply invariant under translations. This paper generalizes the construction so that translations may have a nontrivial effect on field components. PACS: 11.30.Cp Lorentz and Poincare invariance

hep-th↗

arXiv2007

A Derivation of Vector and Momentum Matrices

Given standard angular momentum and boost matrices, the commutation rules for vector and momentum matrices are solved. The resulting matrix components are displayed as detailed functions of spin with factors such as the square root of (2A+1). For comparison and as an alternative, Lyubarskii's formulas in terms of Clebsch-Gordan coefficients are recalled from the literature and displayed. A set of these momentum matrices combined with the corresponding set of six angular momentum and boost matrices form the generators of a nonunitary finite dimensional representation of the Poincare group of translations, rotations and boosts. A problem set is included. PACS: 11.30.Cp Lorentz and Poincare invariance

math-ph↗

arXiv2006

First-Order Field Equations in Spin 1/2 Form

From one point of view in the quantum theory of fields, free quantum fields are uniquely determined, not by field equations, but by the transformations of the field and the annihilation and creation operators from which the field is constructed. One says that a free field equation merely records the fact that some field components are superfluous. Here, free field equations that are first order and covariant are derived so that the already determined field is one solution. The unknowns are the vector matrices that combine with the known gradient of the field to make an invariant equation: the scalar product of the vector matrices and the gradient are proportional to the field. Thus these free field equations are direct consequences of the transformation properties of the annihilation and creation operators and the transformation properties of the field.

hep-th↗