- #1
juliette sekx
- 31
- 0
Hello,
Is there any place I can find the equation for the Taylor expansion of a functional around a function ??
Particularly, I want something like:
[itex]
f[x(t)] = f[\hat{x}(t)] + (f[\hat{x}(t)] - f[x(t)] \frac{\delta f}{\delta x(t)}|_{x(t)=\hat{x}(t)} + \frac{(f[\hat{x}(t)] - f[x(t)])^2}{2!}\frac{\delta ^2f}{\delta ^2x(t)}|_{x(t)=\hat{x}(t)} \ldots
[/itex]
Particularly I want to expand the functional:
[itex]
f[\Psi] [/itex] around the function [itex]\Psi \Psi^*[/itex] where [itex]\Psi^*[/itex] is the compex conjugate
Is there any place I can find the equation for the Taylor expansion of a functional around a function ??
Particularly, I want something like:
[itex]
f[x(t)] = f[\hat{x}(t)] + (f[\hat{x}(t)] - f[x(t)] \frac{\delta f}{\delta x(t)}|_{x(t)=\hat{x}(t)} + \frac{(f[\hat{x}(t)] - f[x(t)])^2}{2!}\frac{\delta ^2f}{\delta ^2x(t)}|_{x(t)=\hat{x}(t)} \ldots
[/itex]
Particularly I want to expand the functional:
[itex]
f[\Psi] [/itex] around the function [itex]\Psi \Psi^*[/itex] where [itex]\Psi^*[/itex] is the compex conjugate