A Canonical perturbation for infinite chain

AI Thread Summary
The discussion revolves around the challenges of applying canonical perturbation theory to an infinite chain of harmonic oscillators, particularly in defining the averaging of functions with infinite angles. The original poster questions whether a theory exists for canonical perturbation in systems with infinite degrees of freedom. They also inquire about the applicability of canonical perturbation theory to classical field theory, suggesting it may serve as an infinite limit of finite systems. Participants are encouraged to share insights or existing theories related to these topics. The conversation highlights the complexities of extending classical perturbation methods to infinite-dimensional systems.
andresB
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I've been Dealing with a problem of perturbation of the movement of an infinite chain of harmonic oscillator and I tried to apply the von Zeippel-Poincare formalism of canonical perturbation theory just to see what I get. This was too naive since I quickly stumbled into the problem of defining the averaging of a function when there are infinite angles to average.

So, does anyone know if there is a theory of canonical perturbation theory for systems with infinite degrees of freedom?
 
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How about classical field theory? It may be thought as the infinite limit of a classical system with finite degrees of freedom.
 
It might be something Do you know a canonical perturbation theory for classical field theory?
 
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