Are non-perturbative methods in physics limited to quantum physics?

[ohwilleke]

TL;DR Summary

Non-perturbative methods are critical is some parts of quantum physics, but it isn't clear to me if they are ever present in classical physics.

Non-perturbative methods are critical in parts of quantum field theory, such as QCD, and have at least some applications in quantum electrodynamics. You can also have mathematical problems that don't have perturbative solutions.

But, it isn't clear to me if classical physics can ever have non-perturbative solutions, and I'm not sure how to find an answer.

In particular, I'm interested in whether non-perturbative effects can be present in general relativity, or if, in the area of gravity, that are necessarily confined to quantum gravity theories.

 

[anuttarasammyak]

Criticality of second phase transition in statistical physics may belong to what you are looking for.

 

[Demystifier]

But, it isn't clear to me if classical physics can ever have non-perturbative solutions, and I'm not sure how to find an answer.

Of course. For example, many QFT books have chapters on topological solutions such as solitons, instantons and magnetic monopoles, which are classical non-perturbative solutions.

In particular, I'm interested in whether non-perturbative effects can be present in general relativity

Of course. The classic examples are Schwarzschild, Reissner-Nordstrom and Kerr solution.

 

[haushofer]

In the context of water waves I found e.g. this paper on nonperturbative stabilization of rogue waves:

https://arxiv.org/abs/1408.3058

 

[A. Neumaier]

it isn't clear to me if classical physics can ever have non-perturbative solutions

There is a huge amount of work on completely integrable systems. Many of them are related to problems of physics.