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自由标量场是不是有无穷多个守恒流?
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轩轩 发表文章数: 1352 |
自由标量场是不是有无穷多个守恒流? dirac场是不是也可以构造无穷多个守恒流? 但从数学角度,不考虑有没有物理 http://zhangxuanzhong.blog.edu.cn/ 《相对论通俗演义》 i will love you till the null infinity.
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sage 发表文章数: 1125 |
Re: 自由标量场是不是有无穷多个守恒流? depends on how many symmetries you have for your lagrangian.
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轩轩 发表文章数: 1352 |
Re: 自由标量场是不是有无穷多个守恒流? 什么是它的对称性?? 据说kdv这样的非线性可积的方程,它无穷多个守恒流。它的对称性比一般场多?? http://zhangxuanzhong.blog.edu.cn/ 《相对论通俗演义》 i will love you till the null infinity.
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卢昌海 发表文章数: 1617 |
Re: 自由标量场是不是有无穷多个守恒流? How many conserved currents a symmetry leads to depends on the corresponding algebra of that symmetry. For instance the conformal symmetry in 2-D conformal field theory corresponding to an infinite-dimensional algebra, therefore there are infinite number of conserved currents (this probably answers what your title asks). Dirac equation, as far as I know, doesn't have any symmetry that corresponding to infinite-dimensional algebra, therefore doesn't have infinite number of conserved currents (I could be wrong on this particular comment about Dirac field, but the general idea is as described above). 宠辱不惊,看庭前花开花落 去留无意,望天空云卷云舒
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轩轩 发表文章数: 1352 |
Re: 自由标量场是不是有无穷多个守恒流? thanks changhai i read a book ,where the lagrangian contains a pair of scalar fields . the two scalar fields are free fields ,but it said it will result in an infinte conserved current. http://zhangxuanzhong.blog.edu.cn/ 《相对论通俗演义》 i will love you till the null infinity.
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kanex 发表文章数: 860 |
Re: 自由标量场是不是有无穷多个守恒流? 守恒流? 很直接啊,dirac field的两个对称是 phi -> e^(i*theta) * phi 和 phi -> e^(i*theta*gamma^5) * phi,所以在经典力学下对应的J_mu = phi横 gamma^mu phi,J_5 = phi横 gamma^mu gamma^5 phi。 不过,由于路径积分中chiral anomaly的存在,如果fix gauge保证J_mu守恒的话,J_5这个axial current是不守恒的。 江畔何人初见月`江月何年初照人`
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