All Questions
6 questions
2votes
0answers
60views
From real variables function to complex variables function?
I'm confused with notations physicists using. They change real variables $$(x_1,x_2,...,x_n)\in (\mathbb{R^2})^n$$ of a function to complex variables $$(z_1,z_1^*,z_2,z_2^*,...,z_n,z_n^*)\in(\mathbb{C^...
2votes
0answers
210views
Properties of analytic continuation of two point/ Wightman function
In this paper, the author considers Wightman functions calculated on an accelerating detector for a massless scalar field, namely $$G_+^R = {}_M \langle 0 | \phi(x) \phi^{\dagger}(x') | 0 \rangle_M$$ $...
- 2,040
0votes
0answers
74views
Kramers-Kronig relations for geometric series
Suppose $\phi(z)$ is an analytic function in the upper complex plane, so it satisfies the Kramers-Kronig relations, i.e. \begin{equation} \Re\phi(w) = \frac{1}{\pi}\int \frac{\Im\phi(x)}{x-w} dx \end{...
- 117
3votes
2answers
888views
Klein-Gordon equation multiple Green's functions
I am trying to understand Green's functions for a Klein-Gordon equation: $ (\frac{\partial^2}{\partial t^2} - \nabla^2 +m^2) \phi(\vec{x},t) = 0$ and $ (\frac{\partial^2}{\partial t^2} - \nabla^2 +...
- 61
1vote
1answer
59views
Change sign for response function
There is a argument about response function: according to the Kramers-Kronig relation$$G(\omega)=\int_{-\infty}^{+\infty}d\omega' \frac{A(\omega')}{\omega+i0_+-\omega'}$$ response function will change ...
- 1,682
36votes
3answers
7kviews
What do the poles of a Green function mean, physically?
Is there a physical interpretation of the existence of poles for a Green function? In particular how can we interpret the fact that a pole is purely real or purely imaginary? It's a general question ...
- 1,001
