不做积分时,
泛函导数与偏导数的差别是前者多出一个 delta function 因子, 这是因为 "同一点才有值".
The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a function with respect to a variable, one differentiates a functional with respect to a function. The definition for the univariate case is
For example, the Euler-Lagrange differential equation is the result of functional differentiation of the Hamiltonian action (functional).
http://spe.sysu.edu.cn/spe/electrodynamics/web/pdf/ext/action.pdf
求能动张量与作用量之间的关系的物理意义
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- 台湾PiPi
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ExtraDim10
Functional Derivative
The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a function with respect to a variable, one differentiates a functional with respect to a function. The definition for the univariate case is
For example, the Euler-Lagrange differential equation is the result of functional differentiation of the Hamiltonian action (functional).
The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a function with respect to a variable, one differentiates a functional with respect to a function. The definition for the univariate case is
For example, the Euler-Lagrange differential equation is the result of functional differentiation of the Hamiltonian action (functional).
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- 一直想思考
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SUSY9
首先物质能动张量的原始定义依赖于时空symmetry.平移or转动。
而等效原理告诉我们引力质量和惯性质量相等。对于某共动观者那么T^(00)这个有平移对应的惯性质量，可以看成引力质量（即几何质量）与g^(00)耦合在一起。一般情况下，即g_ab和T^ab耦合。因此，我们可以变分g_ab给出另一种定义。
而等效原理告诉我们引力质量和惯性质量相等。对于某共动观者那么T^(00)这个有平移对应的惯性质量，可以看成引力质量（即几何质量）与g^(00)耦合在一起。一般情况下，即g_ab和T^ab耦合。因此，我们可以变分g_ab给出另一种定义。
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- 剑圣柏杨
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SUSY9
我没记错的话似乎应该是这个表达式，看起来和一楼的不太一样。我没尝试这两个式子是不是等价的，LZ可以试试看
T^μν = (2/√(-g)) {δ[L_m * √(-g)]/δ[g_μν]}
这个式子导出只需对Hilbert作用量作变分即可
T^μν = (2/√(-g)) {δ[L_m * √(-g)]/δ[g_μν]}
这个式子导出只需对Hilbert作用量作变分即可
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