- #1
robousy
- 334
- 1
Hey folks!
I'm starting with the Lagrangian of a massive scalar field and have found an expression for the expectation value of the energy-momentum tensor.
[tex]<T_{\mu \nu}>=(\partial_\mu \partial_\nu-\frac{1}{2}(g_{\mu \nu}(\partial_\mu \partial_\nu+m^2))G(x-x')[/tex]
let say I have some Green Function G(x-x') and then I compactify the dimension into a circle or radius R, then can someone explain why we write the GF as:
[tex]G(x-x')=\sum_{n=1}^\infty G_\infty(x-x'+2\pi R n \hat{y})[/tex]
And explain the phrase: the Casimir energy can be easily obtained by summing over the infinite volume Green Function over all the images.
What are the images here?
Any help appreciated!
I'm starting with the Lagrangian of a massive scalar field and have found an expression for the expectation value of the energy-momentum tensor.
[tex]<T_{\mu \nu}>=(\partial_\mu \partial_\nu-\frac{1}{2}(g_{\mu \nu}(\partial_\mu \partial_\nu+m^2))G(x-x')[/tex]
let say I have some Green Function G(x-x') and then I compactify the dimension into a circle or radius R, then can someone explain why we write the GF as:
[tex]G(x-x')=\sum_{n=1}^\infty G_\infty(x-x'+2\pi R n \hat{y})[/tex]
And explain the phrase: the Casimir energy can be easily obtained by summing over the infinite volume Green Function over all the images.
What are the images here?
Any help appreciated!