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 an abelian Lie group as structure group, its Lie algebra is also abelian and hence all Lie brackets vanish and makes the Yang-Mills equation reduce to the Maxwell equation:
Let:
be a generalized Laplace operator.
The Bianchi identity and the Yang-Mills equation combine to:
(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 Yang-Mills equations. Recent references include
There is an old review,
that provides some of the known solutions of 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 ‘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 25, 2024 at 15:07:17. See the history of this page for a list of all contributions to it.