Abstract:
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). A computer program is included that, given p and q, calculates the basis matrices.

Abstract:
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.

Abstract:
Some facts about 4-spinors listed and discussed. None, well perhaps some, of the work is original. However, locating formulas in other places has proved a time-consuming process in which one must always worry that the formulas found in any given source assume the other metric (I use {-1,-1,-1,+1}) or assume some other unexpected preconditions. Here I list some formulas valid in general representations first, then formulas using a chiral representation are displayed, and finally formulas in a special reference frame (the rest frame of the `current' j) in the chiral representation are listed. Some numerical and algebraic exercises are provided.

Abstract:
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 energies due to the uncertainty principle. Long collapse times give negligible uncertainty, so the pre-collapse spectrum must approach that of isolated nuclei. We calculate the post-collapse electron spectrum which shows a collapse-dependent pileup near the endpoint. Comparison with observation shows that a collapse time of 1 x 10^-17 s explains the observed pileup. The collapse of the entangled quantum system must be triggered by the environment: most likely an atomic (molecular) electron initially bound to the atomic (molecular) tritium source or perhaps ambient gas molecules. Coincidentally, the 40 eV tritium atom-helium ion energy level shift is unobservably small for times shorter than the system collapse time. We conclude that an atomic (molecular) electron triggers the collapse once the 40 eV shift becomes detectible and the electron detects the helium nucleus. Thus collapse may explain the tritium endpoint pileup.

Abstract:
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).

Abstract:
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).

Abstract:
An electron neutrino can have the quantum phase of an electron, i.e. share its internal clock, if the neutrino takes a path in space-time that is not in the direction of its energy-momentum. Each flavor neutrino would then have a different internal clock; a muon neutrino would have a muon clock and a tau neutrino would have a tau clock. Perhaps surprisingly, there is some evidence suggesting neutrinos have such clocks. If muon neutrinos travel on space-like paths then some atmospheric muon neutrinos would take such paths backwards into outer space and not be observed. These are lost at the source and have nothing to do with oscillations or flavor-changing in flight. The expected depletion of source muon neutrinos is shown here to be 9%, which accounts for half of the missing muon neutrino source flux reported by Super-Kamiokande. Since there is no depletion in the electron neutrino flux source reported at SK and SN1987A electron neutrinos seem to have traveled at the speed of light, the electron neutrino travels on a light-like path. Accelerator-based experiments could be arranged to confirm the reverse motion of muon neutrinos.

Abstract:
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.

Abstract:
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 have different masses. Any free particle spin 1/2 wave function is a sum of plane waves with spin parallel to velocity. Each plane wave, a pair of 2-component rotation eigenvectors, can be associated with a 2x2 matrix representation of rotations in a Euclidean space without disturbing the plane wave's space-time properties. In a space with more than four dimensions, only rotations in a 4d subspace can be represented. So far all is well known. Now consider that unrepresented rotations do not have eigenvectors, do not make plane waves, and do not contribute phase. The particles e, $\pi,$ and p are assigned rotations in a 4d subspace of 16d, rotations in an 8d subspace of 12d, and rotations in a 12d subspace of 12d, respectively. The electron 4d subspace, assumed to be as likely to align with any one 4d subspace as with any other, produces phase when aligned with the represented 4d subspace in 16d. Similarly, we calculate the likelihood that a 4d subspace of the pion's 8d space aligns with the represented 4d subspace in 12d. The represented 4d subspace is contained in the proton's 12d space, so the proton always acquires phase. By the relationship between mass and phase, the resulting particle phase ratios are the particle mass ratios and these are coincident with the measured mass ratios, within about one percent. 1999 PACS number(s): 03.65.Fd Keywords:Algebraic methods; particle masses; rotation group

Abstract:
We continue to derive spacetime quantities and spin 1/2 propagators from rotations. Rotation-invariant projection operators are found for each element of a four element basis, i.e. a basis for four component quantities with specific transformation rules under rotations. With these four projection operators, we make two spacetime invariant projection operators, i.e. once space, time, energy, and momentum are identified. The spacetime invariant operators are propagators for free neutrinos. Except for the substitute basis, the process is the same as the one that gave electron propagators in Part I. PACS number(s): 11.30.-j, 11.30.Cp, and 03.65.Fd