Analytic properties of amplitudes

In summary, the speaker is looking for a resource explaining the analytic properties of Feynman diagrams and their resulting amplitudes. They understand the general concept, but are unsure how to see it from mathematical expressions. They are specifically interested in examples from Non-Abelian gauge theories, such as QCD. The suggested resources are the TOC of a book on Amazon and two other books by Nakanishi and Speer.
  • #1
omrihar
7
1
Hey,

I have been looking around for a good resource explaining the analytic properties of Feynman diagrams and their resulting amplitudes.

I think I understand in general what to expect (branch cuts for multiparticle states, poles for single particle states and bound states), but I'm not sure exactly how to see this from the mathematical expressions.

Does any of you know a good resource explaining how these properties can be seen from the calculations? Preferable a source with many examples (including if possible examples from Non-Abelian gauge theories - specifically QCD).

Thanks!
 
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  • #3
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1. What are analytic properties of amplitudes?

Analytic properties of amplitudes refer to the mathematical properties that describe how the amplitude of a physical quantity varies with changes in its input parameters. These properties include analyticity, unitarity, crossing symmetry, and Regge behavior.

2. Why are analytic properties of amplitudes important?

Analytic properties of amplitudes are important because they can provide insights into the underlying physics governing a physical process. They also play a crucial role in the development and testing of theoretical models, and can be used to make predictions for future experiments.

3. How are analytic properties of amplitudes studied?

Analytic properties of amplitudes are studied using mathematical tools such as complex analysis, perturbation theory, and dispersion relations. These tools allow scientists to analyze the behavior of amplitudes in different regions of parameter space and make predictions for their behavior in unexplored regions.

4. What is the physical significance of analyticity?

The physical significance of analyticity lies in its connection to causality. Analyticity requires that the amplitude of a physical process is smooth and continuous, which is necessary for the process to be physically realizable. Violation of analyticity would imply the existence of unphysical processes and would lead to inconsistencies in our understanding of the physical world.

5. Can analytic properties of amplitudes be experimentally tested?

Yes, analytic properties of amplitudes can be experimentally tested through high energy particle collisions. By measuring the scattering amplitudes of particles at different energies and angles, scientists can confirm the existence of analyticity and other properties, and use them to validate or rule out theoretical models.

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