F-Yang-Mills场的间隙性和不稳定性性质
摘要
用F(‖R▽‖2/2)替换Yang-Mills泛函的积分,我们得到了F-Yang-Mills泛函,进而得到F-Yang-Mills场,这里的F是一个非负且C∞的函数。本文计算了F-Yang-Mills场的第一和第二变分,并研究了欧氏空间和球面的子流形上的F-Yang-Mills场的间隙性和不稳定性质。在文章的最后,我们研究了F-Yang-Mills场得特殊例子——指数-Yang-Mills场。
Replacing the integrand of the Yang-Mills functional by F(‖R▽‖2/2) define an F-Yang-mills functional,and hence F-Yang-Mills fields,where F is a non-negative and C∞function.The first and second variations are calculated,the gaps and instabilities of F-Yang-Mills fields on some submanifolds of the Euclidean spaces and the spheres are investigated.In the last, we studied exp-Yang-Mills fields,which is a special case of F-Yang-Mills fields.
Replacing the integrand of the Yang-Mills functional by F(‖R▽‖2/2) define an F-Yang-mills functional,and hence F-Yang-Mills fields,where F is a non-negative and C∞function.The first and second variations are calculated,the gaps and instabilities of F-Yang-Mills fields on some submanifolds of the Euclidean spaces and the spheres are investigated.In the last, we studied exp-Yang-Mills fields,which is a special case of F-Yang-Mills fields.
引文
[1]陈维桓,李兴校,《黎曼几何引论》上、下册,北京：北京大学出版社,2005
[2]J.-P.Bourguignon and H.B.La wson,Stability and isolation phenomena for Yang-Mills fields.Comm.Math.Phys.79(1981),no.2,189-230
[3]Qun Chen and Zhen-Rong Zhou, On Gap Properties and Instabilities of p-Yang-Mills Fields.Canad.J.Math.Vol.59(6),2007 pp.1245-1259
[4]Y.L.Xin,Instability theorems of Yang-Mills fields.Acta Math.Sci.3(1983),no.1,103-112.
[5]J.-P.Bourguignon,H.B.La wson and J.Simon,Stabilty and gap phenomena for Yang-Mills filed.Proc.Nat.Acad.Sci.U.S.A.76(1979),no.4,1550-1553.
[6]忻元龙,《调和映射》,上海科学技术出版社,1995
[2]J.-P.Bourguignon and H.B.La wson,Stability and isolation phenomena for Yang-Mills fields.Comm.Math.Phys.79(1981),no.2,189-230
[3]Qun Chen and Zhen-Rong Zhou, On Gap Properties and Instabilities of p-Yang-Mills Fields.Canad.J.Math.Vol.59(6),2007 pp.1245-1259
[4]Y.L.Xin,Instability theorems of Yang-Mills fields.Acta Math.Sci.3(1983),no.1,103-112.
[5]J.-P.Bourguignon,H.B.La wson and J.Simon,Stabilty and gap phenomena for Yang-Mills filed.Proc.Nat.Acad.Sci.U.S.A.76(1979),no.4,1550-1553.
[6]忻元龙,《调和映射》,上海科学技术出版社,1995