Richard Shurtleff
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…
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…
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…
The beta-decay of a tritium nucleus produces an entangled quantum system, a beta electron, a helium nucleus, and an antineutrino. For finite collapse times, the post-collapse beta electron energy can originate from a range of pre-collapse…
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…
Massive spin 1/2 particles require 2-spinors for rotations, 4-spinors for rotations and boosts with parity. Including translations requires 8-spinors. Adapting 4-spinor field theory to 8-spinor fields with translation symmetry is discussed…
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…
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…
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…
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).
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).
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…
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…
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…
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…
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…
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.…
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…
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…
Mass is proportional to phase gain per unit time; for e, $\pi$, and p the quantum frequencies are 0.124, 32.6, and 227 Zhz, respectively. By explaining how these particles acquire phase at different rates, we explain why these particles…