6,826 research outputs found

### Non-abelian Eikonals

A functional formulation and partial solution is given of the non-abelian
eikonal problem associated with the exchange of non-interacting, charged or
colored bosons between a pair of fermions, in the large $s$/small $t$ limit. A
simple, functional ``contiguity" prescription is devised for extracting those
terms which exponentiate, and appear to generate the leading, high-energy
behavior of each perturbative order of this simplest non-abelian eikonal
function; the lowest non-trivial order agrees with the corresponding SU(N)
perturbative amplitude, while higher-order contributions to this eikonal
generate an ``effective Reggeization" of the exchanged bosons, resembling
previous results for the perturbative amplitude. One exact and several
approximate examples are given, including an application to self-energy
radiative corrections. In particular, for this class of graphs and to all
orders in the coupling, we calculate the leading-log eikonal for SU(2). Based
on this result, we conjecture the form of the eikonal scattering amplitude for
SU(N).Comment: 19 pages, late

### Possibilities of a QED-Based Vacuum Energy

A QED-based bootstrap mechanism, appearing at sufficiently small space-time
scales, is suggested as an explanation for the "dark" vacuum energy that may be
able to accelerate the universe. Very small-scale vacuum currents are allowed
to generate small-scale electromagnetic fields, which become significant near
the light cone. The resulting lepton-pair production, some of which may be
tachyonic, has ramifications for the convergence of all QED perturbative
processes, as well as providing possible mechanisms for "dark" matter, galactic
gamma-ray bursts, and ultra-high-energy cosmic rays.Comment: 20 pages, 1 tabl

### QED vacuum loops and Inflation

A QED-based model of a new version of Vacuum Energy has recently been
suggested, which leads to a simple, finite, one parameter representation of
Dark Energy. An elementary, obvious, but perhaps radical generalization is then
able to describe both Dark Energy and Inflation in the same framework of Vacuum
Energy. One further, obvious generalization then leads to a relation between
Inflation and the Big Bang, to the automatic inclusion of Dark Matter, and to a
possible understanding of the birth (and death) of a Universe.Comment: 10 pages and 1 figure There has been a minor modification in the
previous version (arXiv:1403.2651v1, 03/12/2014) : a reference has been added
in [3] and an Appendix has been adde

### The Birth and Death of a Universe

This letter is meant to be a brief survey of several recent publications
providing a simple, sequential explanation of Dark Energy, Inflation and Dark
Matter, which leads to a simple picture of the why and the how of the Big Bang,
and thence to a possible understanding of the birth and death of a Universe.Comment: 4 pages, 1 figur

### Alternating groups and moduli space lifting Invariants

Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of
degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves
Fried-Serre on deciding when sphere covers with odd-order branching lift to
unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on
Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces
of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp.
odd) theta functions when r is even (resp. odd). For inner spaces the result is
independent of r. Another use appears in,
http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of
families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for
the prime p=2 lying over Hurwitz spaces first studied by,
http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and
Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*)
High tower levels are general-type varieties and have no rational points.For
infinitely many of those MTs, the tree of cusps contains a subtree -- a spire
-- isomorphic to the tree of cusps on a modular curve tower. This makes
plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs.
Establishing these modular curve-like properties opens, to MTs, modular
curve-like thinking where modular curves have never gone before. A fuller html
description of this paper is at
http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from
proof sheets, but does include some proof simplification in \S

### Non trivial generalizations of the Schwinger pair production result

We present new, non trivial generalizations of the recent Tomaras, Tsamis and
Woodard extension of the original Schwinger formula for charged pair production
in a constant field.Comment: 11 page

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