Home > Q-6 Sitemap

 Next Page

 Previous Page


Top of This Page

Top of This Page wwwDGrammaticalPhysicsDac | Siteowner

ySEOtextz0. General Formulation, (2) Continuous System, Consider the special case: I()=dtL(*(t,*),0*(t,*)),ӁRn(R4),LR(Rn(R3),Rn(R3)) The functional L is called Lagrangian of the system. (i) Euler-Lagrange Equation I()/ƒӃ(x)=0̃L(*(t,*),0*(t,*))/[*(t,*)](x)-d/dtL(*(t,*),0*(t,*))/[0*(t,*)](x)=0 (ii) Local Field Theory, Consider the special case: L(,)=d3xL(*(x);*(x),݃*(x)), ,ՁRn(R3); LR(Rn;Rn,R3~n) The function L is called Lagrangian density of the system. a. I()=d4xL(*(x);**(x)) b. I()/ƒӃ(x)=0́L(*(x);**(x))/݃Ӄ(x)-/xʁL(*(x);**(x))/[݃ʃӃ(x)]=0 c. Noether's Theorem for Local Field Theory, Assumption, If I()/ƒӃ(x)=0 then: ̓R4; (/݃)I('*(*;,);'(,))|=0=0 where: I(;)=xd4xL(*(x),**(x))

(C) Yuuichi Uda. All rights reserved.