- #1

parton

- 83

- 1

In the literature (Ryder, path-integrals) I have found the following relation for the functional derivative with respect to a real scalar field [tex] \phi(x) [/tex]:

[tex] i \dfrac{\delta}{\delta \phi(x)} e^{-i \int \mathrm{d}^{4} x \frac{1}{2} \phi(x) ( \square + m^2 ) \phi(x)} = ( \square + m^2 ) \phi(x) e^{-i \int \mathrm{d}^{4} x \frac{1}{2} \phi(x) ( \square + m^2 ) \phi(x)}[/tex]

But how do I compute this? I am just confused about this d'Alembert operator [tex] \square [/tex] and I never end up with the right solution as above.

Could anybody explain how to obtain this solution, please?

[tex] i \dfrac{\delta}{\delta \phi(x)} e^{-i \int \mathrm{d}^{4} x \frac{1}{2} \phi(x) ( \square + m^2 ) \phi(x)} = ( \square + m^2 ) \phi(x) e^{-i \int \mathrm{d}^{4} x \frac{1}{2} \phi(x) ( \square + m^2 ) \phi(x)}[/tex]

But how do I compute this? I am just confused about this d'Alembert operator [tex] \square [/tex] and I never end up with the right solution as above.

Could anybody explain how to obtain this solution, please?

Last edited: