calculus of variations - What is the functional derivative ...
2020年4月4日 · as I understood, the term on the RHS is the functional derivative. But since the LHS is a functional and the RHS is a functional + a real number ($\epsilon$) times the functional derivative, I conclude that the functional derivative must also be a functional. Functions/Distributions. The english wikipedia page [2] states, that the functional ...
Definition of functional derivative - Mathematics Stack Exchange
2017年3月25日 · A functional derivative normally gives you as output not a function, but a differential equation with ...
Functional Derivative of action - Physics Stack Exchange
2016年1月13日 · Now I take the functional derivative $\frac{\delta S[\phi]}{\delta\phi(x)}$ to get $\frac{\delta S[\phi]}{\delta\phi(x)}=-\frac{1}{2}(\partial_\mu\partial^\mu\phi(x)+2m^2\phi(x))$ Setting this equal to zero should give me the Klein-Gordon equation, but …
lagrangian formalism - How to calculate functional derivative …
2020年12月29日 · Here is a second way to see the correct result for taking the functional derivative of the spacetime derivative of the field, which I hope will be helpful. Recall that the definition of the functional derivative is $$ \frac{\delta\phi(y)}{\delta\phi(x)}=\delta(y-x) .$$ You know that Dirac deltas are distributions. That is, you should always ...
Functional Derivative - Physics Stack Exchange
2020年4月11日 · The reason for that is because Lancaster is calculating the functional derivative: $$ \tag{1} \frac{1}{\epsilon} \lim_{\epsilon \rightarrow 0} \int \left( g[f(x) + \epsilon \delta(x-x_0)] - g[f(x)] \right) \mathrm{d}x $$ and here it is sufficient to take only the first (and zeroth) term of the Taylor series because all the other term will not ...
homework and exercises - Taking functional derivatives of …
2021年4月30日 · A functional derivative is a natural continuation of the concept of a multivariable derivative to an ...
Functional derivative and first variation - Mathematics Stack …
2021年3月8日 · Related to this contradiction I have a general question of understanding. If the functional derivative is the analogue to partial derivatives, and the first variation the analogue to a total differential, what, in calculus of variations, is the analogue to a total derivative? We speak of F[y] as being differentiable, but there is no total ...
calculus of variations - Functional derivatives in (Physics) Field ...
Nevertheless, be aware that many authors confusingly use the 'same-time' functional derivative (7) as a shorthand notation for the Euler-Lagrange expression (4), or the functional derivative (3), cf. e.g. my Phys.SE answers here and here.--$^1$ Note however, that in field theory (as opposed to point mechanics) that a functional derivative
Functional Taylor series - Mathematics Stack Exchange
2016年8月24日 · Functional derivative of a functional that depends on antiderivative. 1. Functional derivative and first ...
calculus of variations - How to calculate this functional derivative ...
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