Canonical perturbation for infinite chain

In summary, the conversation discusses the topic of applying the von Zeippel-Poincare formalism of canonical perturbation theory to a problem involving an infinite chain of harmonic oscillator. However, the conversation quickly touches upon the issue of defining the averaging of a function when there are infinite angles to average. The question is posed if there is a theory of canonical perturbation theory for systems with infinite degrees of freedom, specifically in the context of classical field theory. The idea of classical field theory being the infinite limit of a classical system with finite degrees of freedom is also mentioned. The final question is if there exists a canonical perturbation theory for classical field theory.
  • #1
andresB
626
374
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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  • #2
How about classical field theory? It may be thought as the infinite limit of a classical system with finite degrees of freedom.
 
  • #3
It might be something Do you know a canonical perturbation theory for classical field theory?
 

Related to Canonical perturbation for infinite chain

What is "Canonical perturbation for infinite chain"?

Canonical perturbation for infinite chain is a mathematical method used to analyze and describe the dynamics of a system with an infinite number of particles or components. It is based on the principles of classical mechanics and is commonly used in fields such as physics, chemistry, and engineering.

How does canonical perturbation for infinite chain differ from other perturbation methods?

Canonical perturbation for infinite chain is unique in that it takes into account the interactions between an infinite number of particles, rather than just a small number. This allows for a more accurate and comprehensive analysis of the system's dynamics.

What are some real-world applications of canonical perturbation for infinite chain?

Canonical perturbation for infinite chain has many practical applications, including in the study of crystal structures, polymer chains, and other complex systems. It is also used in the field of celestial mechanics to model the movement of celestial bodies.

What are the limitations of canonical perturbation for infinite chain?

One limitation of canonical perturbation for infinite chain is that it is only applicable to systems with known equations of motion. It also assumes that the system is in a state of equilibrium, which may not always be the case.

Are there any alternative methods to canonical perturbation for infinite chain?

Yes, there are other perturbation methods that can be used for systems with an infinite number of components, such as the Lindstedt-Poincaré method and the averaging method. These methods have their own advantages and limitations, and the choice of method depends on the specific system being studied.

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