General Selfdual Yang-Mills Solutions
May, 197840 pages
Published in:
- Phys.Rev.D 18 (1978) 2013
Report number:
- CU-TP-119
Citations per year
Abstract: (APS)
The recent work of Atiyah, Hitchin, Drinfeld, and Manin is used to discuss self-dual Yang-Mills solutions for the compact gauge groups O(n), SU(n), and Sp(n). It is shown that the resulting solutions contain the correct number of parameters for all values of the topological charge. Although explicit construction of a general self-dual field requires the solution of a finite-dimensional, nonlinear matrix equation, we show that for widely separated instantons this equation can be solved perturbatively, providing a systematic expansion about the dilute-gas limit and a physical interpretation of the independent parameters in this limit. Further, closed-form expressions can be obtained for the general SU(2) solutions with topological charge 2 or 3. Finally, explicit isospin-1/2 and isospin-1 propagators are derived for a massless scalar field in the presence of the general self-dual SU(2) solution.- GROUP THEORY
- SYMMETRY: O(N)
- SYMMETRY: SU(N)
- SYMMETRY: SP(N)
- FIELD THEORETICAL MODEL: YANG-MILLS
- SYMMETRY: SU(2)
- FIELD EQUATIONS: INSTANTON
- CHARGE: TOPOLOGICAL
- FIELD THEORY: SCALAR
- FIELD THEORY: MASSLESS
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