超对称自对偶杨─Mills模型的Hamilton约化

Hamiltonian Reductions of Supersymmetric Self-Dual Yang-Mills Fields

本文研究了４维超对称自对偶杨－Ｍｉｌｌｓ模型的Ｈａｍｉｌｔｏｎ约化．在左右对称的常约束下导出了４维超对称非阿贝尔Ｔｏｄａ模型、相应的作用量以及线性系统．在主阶化下的１阶约束条件下，得到了４维超对称Ｔｏｄａ模型．本文的约化对任意李超代数都成立，并不特别要求李超代数具有纯奇素根系．

The Hamiltonian reductions of supersymmetric self-dual Yang-Mills theory are analysed. Under the left-right dual constant constraints, this theory is reduced to the four dimensional supersymmetric nonabelian Toda model. The corresponding actionand linear systems are also obtained as the result of Hamiltonian reductions. In the case of first order constraints under the principal gradation of the underlying Lie superalgebra, the reduced theory is shown to be the four dimensional supersymmetric Toda model. The reduction procedure apply to any Lie superalgebra without requiring a purely odd simple root system.