Yang-Mills equation in nLab
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Algebraic Quantum Field Theory
algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
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quantum mechanical system, quantum probability
interacting field quantization
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Idea
The Yang-Mills equations are the equations of motion/Euler-Lagrange equations of Yang-Mills theory. They generalize Maxwell's equations.
References
(For full list of references see at Yang-Mills theory)
General
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Karen Uhlenbeck, notes by Laura Fredrickson, Equations of Gauge Theory, lecture at Temple University, 2012 (pdf, pdf)
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DispersiveWiki, Yang-Mills equations
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TP.SE, Which exact solutions of the classical Yang-Mills equations are known?
Solutions
General
Wu and Yang (1968) found a static solution to the sourceless Yang-Mills equations. Recent references include
- J. A. O. Marinho, O. Oliveira, B. V. Carlson, T. Frederico, Revisiting the Wu-Yang Monopole: classical solutions and conformal invariance
There is an old review,
- Alfred Actor, Classical solutions of Yang—Mills theories, Rev. Mod. Phys. 51, 461–525 (1979),
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.
Instantons and monopoles
For Yang-Mills instantons the most general solution is known, first worked out by
- Michael Atiyah, Nigel Hitchin, Vladimir Drinfeld, Yuri Manin, Construction of instantons, Physics Letters 65 A, 3, 185–187 (1978) pdf
for the classical groups SU, SO , Sp, and then by
- C. Bernard, N. Christ, A. Guth, E. Weinberg, Pseudoparticle Parameters for Arbitrary Gauge Groups, Phys. Rev. D16, 2977 (1977)
for exceptional Lie groups. The latest twist on the Yang-Mills instanton story is the construction of solutions with non-trivial holonomy:
- Thomas C. Kraan, Pierre van Baal, Periodic instantons with nontrivial holonomy, Nucl.Phys. B533 (1998) 627-659, hep-th/9805168
There is a nice set of lecture notes
- David Tong, TASI Lectures on Solitons (hep-th/0509216),
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 06:55:38. See the history of this page for a list of all contributions to it.