Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 but I would be interested in the interpretation in quantum systems.

share|cite|improve this question
Can you be more specific and maybe give an example from Quantum Mechanics? – Turion Jun 5 '12 at 8:42

The pole of Green's function is related to the spectrum of the particle which is propagating. One dimension for example $$\tilde{G}(\omega)= \frac{i}{\omega-(\epsilon+i\Gamma)}$$ If pure real, G(t) is some oscillation function which shows that the particle is stable. If pure imaginary, G(t) has some exponential decay behavior which shows that the particle is unstable.

share|cite|improve this answer
For classical linear response the GF can be neither purely real nor purely imaginary on any finite interval because of Kramers-Kronig. I.e., a real GF violates causality except in vacuum. Is this not true in QM? – user27777 Aug 12 '13 at 15:22
The picture is similar. For free case without interaction, GF is real. For intacting case, there is a imaginary part which is related to self energy. Linear response is some kinds of interacting. – Craig Thone Aug 13 '13 at 3:07

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.