10 research outputs found
A Nonabelian Yang-Mills Analogue of Classical Electromagnetic Duality
The classic question of a nonabelian Yang-Mills analogue to electromagnetic
duality is here examined in a minimalist fashion at the strictly 4-dimensional,
classical field and point charge level. A generalisation of the abelian Hodge
star duality is found which, though not yet known to give dual symmetry,
reproduces analogues to many dual properties of the abelian theory. For
example, there is a dual potential, but it is a 2-indexed tensor
of the Freedman-Townsend type. Though not itself functioning as such,
gives rise to a dual parallel transport, , for the
phase of the wave function of the colour magnetic charge, this last being a
monopole of the Yang-Mills field but a source of the dual field. The standard
colour (electric) charge itself is found to be a monopole of .
At the same time, the gauge symmetry is found doubled from say to
. A novel feature is that all equations of motion,
including the standard Yang-Mills and Wong equations, are here derived from a
`universal' principle, namely the Wu-Yang (1976) criterion for monopoles, where
interactions arise purely as a consequence of the topological definition of the
monopole charge. The technique used is the loop space formulation of Polyakov
(1980).Comment: We regret that, due to a technical hitch, parts of the reference list
were mixed up. This is the corrected version. We apologize to the authors
whose papers were misquote
Neutral-current ratios in three-triplet and three-quarte gauge theories of the weak and electromagnetic interactions
A Generalized duality symmetry for nonabelian Yang-Mills fields
It is shown that classical nonsupersymmetric Yang-Mills theory in 4
dimensions is symmetric under a generalized dual transform which reduces to the
usual dual *-operation for electromagnetism. The parallel phase transport
constructed earlier for monopoles is seen to function also
as a potential in giving full description of the gauge field, playing thus an
entirely dual symmetric role to the usual potential . Sources of
are monopoles of and vice versa, and the Wu-Yang criterion for
monopoles is found to yield as equations of motion the standard Wong and
Yang-Mills equations for respectively the classical and Dirac point charge;
this applies whether the charge is electric or magnetic, the two cases being
related just by a dual transform. The dual transformation itself is explicit,
though somewhat complicated, being given in terms of loop space variables of
the Polyakov type.Comment: Latex file, 26 pages, 3 figures and 2 charts not included but
supplied on reques