The functional-derivatives tag has no wiki summary.
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Derivative of $\epsilon$ in lennard jones equation
I just want to calculate the derivative of epsilon for the following Lennard Jones equation:
LJ = $4\sqrt{\epsilon_{ii} \epsilon_{jj}}$ $[(\sigma/ r)^{12}-(\sigma/r)^{6}]$ with respect to ...
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1answer
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Finding Hamilton's equations given a Hamiltonian
I am trying to find Hamilton's equations for a general Hamiltonian given by $$H[u]=\int_\mathbf{R} \phi(u,u_x)dx$$
Suppose $$\frac{\delta f[u]}{\delta u(x)}\equiv \frac{\partial f}{\partial ...
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Vacuum to vacuum transition amplitude
I have two questions about Vacuum to vacuum transition amplitude.
Can any particle stay in $|0\rangle$?
I was studying this topic from Srednicki's QFT book. He writes in eq.$(6.22)$
$$\langle0|0 ...
2
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2answers
363 views
Field theory:functional derivative involving Fourier Transform
I have to solve the following functional derivative
$$
\frac{\delta}{\delta \Lambda(\mathbf{x})}\log[A-\mathbf{k}^2\Lambda(\mathbf{k})]
$$
where $\Lambda(\mathbf{k})$ is the Fourier transform of ...
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3answers
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Is it safe to ignore derivatives of velocity w.r.t. position and vice versa?
In a certain textbook a function is given as:
$$f=f(x(t))$$
And then this is differentiated w.r.t. $t$ to get:
$$f_t=\dot{x}f_x$$
(Where the notation $f_u=df/du$, $f_{uu}=d^2f/du^2$, etc.)
This ...
4
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1answer
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Functional Derivation of Holonomy
I would like to know how to take the functional derivative of the holonomy, or Wilson line. I have tried it and I will show what I have done below, but before I wanted to say that I also have seen ...
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3answers
437 views
What is the relation between (physicists) functional derivatives and Fréchet derivatives
I´m wondering how can one get to the definition of Functional Derivative found on most Quantum Field Theory books:
$$\frac{\delta F[f(x)]}{\delta f(y) } = \lim_{\epsilon \rightarrow 0} ...
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1answer
63 views
matrix field theory
I am studying a field theory where the field is a matrix. The problem is that I have to calculate some functional derivative. How could we define functional derivative when the field is a matrix ?
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498 views
Introductory texts for functionals and calculus of variation
I am going to learn some math about functionALs (like functional derivative, functional integration, functional Fourier transform) and calculus of variation. Just looking forward to any good ...
