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

In summary, non-perturbative methods are crucial in quantum field theory and have applications in quantum electrodynamics. There can also be mathematical problems without perturbative solutions. It is uncertain if classical physics can have non-perturbative solutions, but there are examples of classical non-perturbative solutions in quantum field theory books. Non-perturbative effects can also be present in general relativity, as seen in the Schwarzschild, Reissner-Nordstrom, and Kerr solutions. There is also a significant amount of research on non-perturbative stabilization of rogue waves in the context of water waves. Additionally, there is a large body of work on completely integrable systems, many of which are relevant to
  • #1
ohwilleke
Gold Member
2,429
1,418
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.
 
  • Like
Likes haushofer
Physics news on Phys.org
  • #2
Criticality of second phase transition in statistical physics may belong to what you are looking for.
 
  • Skeptical
Likes ohwilleke
  • #3
ohwilleke said:
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.
ohwilleke said:
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.
 
  • Like
Likes ohwilleke, haushofer, nnunn and 3 others
  • #5
ohwilleke said:
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.
 

Similar threads

  • Beyond the Standard Models
Replies
1
Views
640
  • Beyond the Standard Models
Replies
10
Views
1K
  • Beyond the Standard Models
Replies
1
Views
2K
  • Beyond the Standard Models
Replies
24
Views
4K
  • Beyond the Standard Models
Replies
19
Views
2K
Replies
5
Views
1K
Replies
2
Views
2K
Replies
3
Views
1K
  • Beyond the Standard Models
Replies
6
Views
1K
  • Beyond the Standard Models
Replies
5
Views
519
Back
Top