1,044,060 research outputs found
Large deviations for the Yang-Mills measure on a compact surface
We prove the first mathematical result relating the Yang-Mills measure on a
compact surface and the Yang-Mills energy. We show that, at the small volume
limit, the Yang-Mills measures satisfy a large deviation principle with a rate
function which is expressed in a simple and natural way in terms of the
Yang-Mills energy
Natural Symmetries of the Yang-Mills Equations
We define a natural generalized symmetry of the Yang-Mills equations as an
infinitesimal transformation of the Yang-Mills field, built in a local, gauge
invariant, and Poincar\'e invariant fashion from the Yang-Mills field strength
and its derivatives to any order, which maps solutions of the field equations
to other solutions. On the jet bundle of Yang-Mills connections we introduce a
spinorial coordinate system that is adapted to the solution subspace defined by
the Yang-Mills equations. In terms of this coordinate system the complete
classification of natural symmetries is carried out in a straightforward
manner. We find that all natural symmetries of the Yang-Mills equations stem
from the gauge transformations admitted by the equations.Comment: 23 pages, plain Te
Yang-Mills theory for non-semisimple groups
For semisimple groups, possibly multiplied by U(1)'s, the number of
Yang-Mills gauge fields is equal to the number of generators of the group. In
this paper, it is shown that, for non-semisimple groups, the number of
Yang-Mills fields can be larger. These additional Yang-Mills fields are not
irrelevant because they appear in the gauge transformations of the original
Yang-Mills fields. Such non-semisimple Yang-Mills theories may lead to physical
consequences worth studying. The non-semisimple group with only two generators
that do not commute is studied in detail.Comment: 16 pages, no figures, prepared with ReVTeX
The Benjamin Loan Mills
Although there was a time when the Benjamin Loan Mills were alive with activity, those days are now gone. They ended a century ago when the gristmill and the sawmill closed in 1901 after yet another fire. When the smoke cleared, Christian Deardorff, the mills\u27 last owner, may have sighed with relief, for he had been trying sporadically to sell the mills for thirteen years, ever since he had rebuilt them after an earlier fire. In 1901, when again faced with fire-damaged mills, Deardorff decided not to rebuild them. In doing so, he also closed the last chapter in the history of these mills. [excerpt
Instantons and Yang-Mills Flows on Coset Spaces
We consider the Yang-Mills flow equations on a reductive coset space G/H and
the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces
G/H one can introduce geometric fluxes identified with the torsion of the spin
connection. The condition of G-equivariance imposed on the gauge fields reduces
the Yang-Mills equations to phi^4-kink equations on R. Depending on the
boundary conditions and torsion, we obtain solutions to the Yang-Mills
equations describing instantons, chains of instanton-anti-instanton pairs or
modifications of gauge bundles. For Lorentzian signature on R x G/H, dyon-type
configurations are constructed as well. We also present explicit solutions to
the Yang-Mills flow equations and compare them with the Yang-Mills solutions on
R x G/H.Comment: 1+12 page
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