Canonical perturbation for infinite chain

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SUMMARY

The discussion centers on the application of canonical perturbation theory, specifically the von Zeippel-Poincare formalism, to an infinite chain of harmonic oscillators. The author encountered challenges in defining the averaging of functions due to the infinite number of angles involved. Participants are seeking insights into whether a canonical perturbation theory exists for systems with infinite degrees of freedom, particularly in the context of classical field theory, which can be viewed as the infinite limit of finite systems.

PREREQUISITES
  • Understanding of canonical perturbation theory
  • Familiarity with harmonic oscillators
  • Knowledge of classical field theory
  • Concept of averaging functions in infinite dimensions
NEXT STEPS
  • Research canonical perturbation theory for infinite-dimensional systems
  • Explore the implications of classical field theory on perturbation methods
  • Study the von Zeippel-Poincare formalism in detail
  • Investigate averaging techniques for functions with infinite variables
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Physicists, mathematicians, and researchers interested in advanced topics in perturbation theory and classical field theory, particularly those working with 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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