algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
The Yang-Mills equations are the equations of motion/Euler-Lagrange equations of Yang-Mills theory. They generalize Maxwell's equations.
(For full list of references see at Yang-Mills theory)
Karen Uhlenbeck, notes by Laura Fredrickson, Equations of Gauge Theory, lecture at Temple University, 2012 (pdf, pdf)
DispersiveWiki, Yang-Mills equations
TP.SE, Which exact solutions of the classical Yang-Mills equations are known?
Wu and Yang (1968) found a static solution to the sourceless $SU(2)$ Yang-Mills equations. Recent references include
There is an old review,
that provides some of the known solutions of $SU(2)$ gauge theory in Minkowski (monopoles, plane waves, etc) and Euclidean space (instantons and their cousins). For general gauge groups one can get solutions by embedding $SU(2)$‘s.
For Yang-Mills instantons the most general solution is known, first worked out by
for the classical groups SU, SO , Sp, and then by
for exceptional Lie groups. The latest twist on the Yang-Mills instanton story is the construction of solutions with non-trivial holonomy:
There is a nice set of lecture notes
on topological solutions with different co-dimension (Yang-Mills instantons, Yang-Mills monopoles, vortices, domain walls). Note, however, that except for instantons these solutions typically require extra scalars and broken U(1)‘s, as one may find in super Yang-Mills theories.
Some of the material used here has been taken from
Another model featuring Yang-Mills fields has been proposed by Curci and Ferrari, see Curci-Ferrari model.
Last revised on November 17, 2019 at 01:55:38. See the history of this page for a list of all contributions to it.