[5] **viXra:1009.0076 [pdf]**
*submitted on 29 Sep 2010*

**Authors:** Philip Gibbs

**Comments:** 7 pages. Published in Prespacetime Journal, Vol. 1, Issue 8, pp. 1218-1224 (2010)

Hyperdeterminants are generalizations of determinants from matrices to multi-dimensional
hypermatrices. They were discovered in the 19th century by Arthur Cayley but were largely
ignored over a period of 100 years before once again being recognised as important in
algebraic geometry, physics and number theory. It is shown that a cubic elliptic curve
whose Mordell-Weil group contains a Z_{2} x Z_{2} x Z subgroup can be transformed into the
degree four hyperdeterminant on a 2x2x2 hypermatrix comprising its variables and coefficients.
Furthermore, a multilinear problem defined on a 2x2x2x2 hypermatrix of coefficients can
be reduced to a quartic elliptic curve whose J-invariant is expressed in terms of the
hypermatrix and related invariants including the degree 24 hyperdeterminant. These
connections between elliptic curves and hyperdeterminants may have applications in
other areas including physics.

**Category:** High Energy Particle Physics

[4] **viXra:1009.0066 [pdf]**
*submitted on 23 Sep 2010*

**Authors:** Alexander G. Kyriakos

**Comments:** 13 pages

The purpose of this chapter of nonlinear theory of elementary particles (NTEP) is to describe the
mechanism of generation of massive elementary particles. The theory, presented below, indicates
the possibility of the particle mass production by means of massive intermediate boson, but without
the presence of Higgs's boson. It is shown that nonlinearity is critical for the appearance of
particles' masses.

**Category:** High Energy Particle Physics

[3] **viXra:1009.0061 [pdf]**
*submitted on 21 Sep 2010*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 15 pages, Also archived as arXiv:1009.3584 [physics.gen-ph].

Recent preliminary data gathered by the Fermilab MINOS Collaboration suggest with 95% confidence
that the mass of the muon neutrino differs from that of its antineutrino partner, which contradicts the
entrenched relativistic quantum theory notion that a free antiparticle is a negative-energy free particle
compelled to travel backwards in time. Also a discrepancy of about five standard deviations in the value
of the proton charge radius recently obtained from muonic hydrogen versus that previously obtained from
electronic hydrogen casts doubt on the calculation of the dominant relativistic QED contributions to
the effects that are actually measured (e.g., the Lamb shift): these QED contributions dominate proton
charge radius contributions less in muonic hydrogen than in electronic hydrogen. The negative-energy "free
particles" of entrenched relativistic quantum theory are well-known features of the Klein-Gordon and Dirac
equations, which are shown to have many other unphysical features as well. The correspondence principle
for relativistic particles is incompatible with these two equations, produces no unphysical features and
implies only positive energies for free particles, which eliminates the very basis of the entrenched notion of
antiparticles, as well as of the CPT theorem. This principle thus requires antiparticles to arise from charge
conjugation (or more generally CP) invariance, whose known breaking is naturally expected to produce
mass splitting between particle and antiparticle, in consonance with the preliminary MINOS data. It also
requires revamping of relativistic QED, which is in accord with the doubt cast on it by the proton charge
radius results, and implies that QED is nonlocal, i.e. has no Hamiltonian density.

**Category:** High Energy Particle Physics

[2] **viXra:1009.0003 [pdf]**
*submitted on 1 Sep 2010*

**Authors:** Bernard Riley

**Comments:**
6 pages, including 3 figures.

In a recent paper, Hooper et al. have shown that the excess of low energy
events observed by the CoGeNT collaboration and the annual modulation
observed for some years by the DAMA and DAMA/LIBRA collaborations
could be explained by a dark matter particle with a mass of approximately
7.0 GeV. Such a dark matter candidate could be the missing particle within
a framework that relates particle masses to the Planck Mass. Massive
particles occupy coincident levels and sublevels within three sequences
that descend in geometric progression, with common ratios 1/π, 2/π and
1/e, from the Planck Mass. The putative fundamental particles are arranged
precisely upon or, in partnership, about mass superlevels and their
coincidences within sequences with common ratios (1/π)^{3}, (2/π)^{3} and (1/e)^{3}.
Four close superlevel coincidences, of which three are occupied, occur
within the range of mass scales from that of the electron to that of the top
quark. The fourth and uniquely precise superlevel coincidence occurs at
7.0 GeV.

**Category:** High Energy Particle Physics

[1] **viXra:1009.0002 [pdf]**
*replaced on 3 Sep 2010*

**Authors:** Fred Alan Wolf

**Comments:**
15 pages

It is shown that the usual quantum field theoretical argument for the vanishing of the
commutator (VC) for spacelike separated fields implying causality is not tenable. For VC to
be tenable negative energy antiparticles traveling forward in time must exist and negative
energy particles traveling backward in time are not allowed. Hence VC denies the existence
of positive energy antiparticles.

**Category:** High Energy Particle Physics