12,675 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 /small 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
Analytic, Non-Perturbative, Gauge-invariant QCD: Nucleon Scattering and Binding Potentials
Removal of the quenched approximation in the mechanism which produced an
analytic estimate of quark-binding potentials, along with a reasonable
conjecture of the color structure of the nucleon formed by such a binding
potential, is shown to generate an effective, nucleon scattering and binding
potential. The mass-scale factor on the order of the pion mass, previously
introduced to define transverse imprecision of quark coordinates, is again
used, while the strength of the potential is proportional to the square of a
renormalized QCD coupling constant. The potential so derived does not include
corrections due to spin, angular momentum, nucleon structure, and electroweak
interactions; rather, it is qualitative in nature, showing how Nuclear Physics
can arise from fundamental QCD.Comment: 25 pages, 3 figures in REVTeX. The fifth of a series on
Non-Perturbative QCD (Eur. Phys. J. C65, 395 (2010) or arXiv:0903.2644
[hep-th], arXiv:1003.2936 [hep-th], arXiv:1103.4179 [hep-th] and
arXiv:1104.4663 [hep-th].
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
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
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
A New Approach to Analytic, Non-Perturbative and Gauge-Invariant QCD
Following a previous calculation of quark scattering in eikonal
approximation, this paper presents a new, analytic and rigorous approach to the
calculation of QCD phenomena. In this formulation a basic distinction between
the conventional "idealistic" description of QCD and a more "realistic"
description is brought into focus by a non-perturbative, gauge-invariant
evaluation of the Schwinger solution for the QCD generating functional in terms
of the exact Fradkin representations of the Green's functional and the vacuum
functional. Because quarks exist asymptotically only in bound states, their
transverse coordinates can never be measured with arbitrary precision; the
non-perturbative neglect of this statement leads to obstructions that are
easily corrected by invoking in the basic Lagrangian a probability amplitude
which describes such transverse imprecision.
The second result of this non-perturbative analysis is the appearance of a
new and simplifying output called "Effective Locality", in which the
interactions between quarks by the exchange of a "gluon bundle" - which
"bundle" contains an infinite number of gluons, including cubic and quartic
gluon interactions - display an exact locality property that reduces the
several functional integrals of the formulation down to a set of ordinary
integrals. It should be emphasized that "non-perturbative" here refers to the
effective summation of all gluons between a pair of quark lines, but does not
(yet) include a summation over all closed-quark loops which are tied by
gluon-bundle exchange to the rest of the "Bundle Diagram". As an example of the
power of these methods we offer as a first analytic calculation the
quark-antiquark binding potential of a pion, and the corresponding three-quark
binding potential of a nucleon, obtained in a simple way from relevant eikonal
scattering approximations.Comment: 38 pages, 3 figures in REVTeX. Collections of follow-on work of Eur.
Phys. J. C65, pp. 395-411 (2010). arXiv admin note: text overlap with
arXiv:1103.4179, arXiv:1104.4663, arXiv:1003.293
Non-perturbative QCD amplitudes in quenched and eikonal approximations
Even though approximated, strong coupling non-perturbative QCD amplitudes
remain very difficult to obtain. In this article, in eikonal and quenched
approximations, physical insights are presented that rely on the
newly-discovered property of Effective Locality.Comment: Revised version (28 pages and 1 figure in REVTeX). Follow-up work of
Eur. Phys. J. C65, pp. 395-411 (2010), (arXiv:1204.2038 [hep-ph]), and Ann.
Phys. 327, pp. 2666-2690 (2012), (arXiv:1203.6137 [hep-ph]
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
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