A Lehmann Kallen and spectral representation

[paralleltransport]

TL;DR

I'd like to better understand the lehmann kallen representation of the propagator.

Hello,

My question pertains to the formula below:

In particular, I would like to ask about the spectral density function shown below:

What does the spectral function physically represent? Is there any interpretation of its meaning, whether it has a relation to the physical spectrum of the theory.

My work:

The propagator real poles correspond to particles (a particle is a lump of energy that doesn't decay or split), it seems to suggest that the spectral function would have delta functions at 1 particle state at rest. Obviously, in a lorentz invariant QFT, one can boost this one particle state to get a continuous spectrum, so \rho(p^2) is not the spectrum of the theory, but it has some relation to it.

Thank you.

 

[malawi_glenn]

Do you have Peskin & Schroeder? Chapter 7

The Lehmann spectral densitity is related to the probablity for a transition from a 1-particle state to a multi-particle state

https://www.cambridge.org/higheredu...ory/5484B936BB6323A0991E334AE9A02A49#overview click on cover to read chapter 1: https://www.book2look.com/book/9781108480901