Classical field models with infinite conserved quantities

Another sufficient condition is that the system allows for Bäcklund transformations, which can generate an infinite number of solitons. However, it is not clear if this is always the case and more research is needed to fully understand the reasons behind this. Other possible sufficient conditions for a system to have infinitely many conserved quantities include being solvable by the inverse scattering method or having an infinite number of symmetries.
  • #1
Othin
36
1
Couldn't really fit the precise question in the title due to the character limit. I want to know what are some sufficient conditions for a model in classical field theory to possesses infinitely many conserved quantities. The sine-Gordon and KdV equations are examples of such systems. Now, intuitely I believe that a system which allows Bäcklund transformations should fit the bill, for we can generate an infinite number of solitons. But I don't know if that's actually right and, if it is, I can't understand the reason as precisely as I would like. Is it? What are [other, if that is indeed one] sufficient conditions for a system to possesses infinitely many conserved quantities?
 
Physics news on Phys.org
  • #2
A:The KdV equation is an example of an integrable system, and sufficient conditions for a classical field theory to possess infinitely many conserved quantities are that it is integrable. These systems can be studied using the inverse scattering transform.
 

1. What are classical field models with infinite conserved quantities?

Classical field models with infinite conserved quantities are mathematical models used to describe physical systems with an infinite number of conserved quantities. These models are based on classical field theory, which is a branch of physics that studies systems with an infinite number of degrees of freedom.

2. Why are these models important in physics?

These models are important in physics because they provide a framework for understanding and predicting the behavior of complex physical systems. They also play a crucial role in many areas of physics, such as quantum field theory and statistical mechanics.

3. What are some examples of classical field models with infinite conserved quantities?

Some examples of classical field models with infinite conserved quantities include the Klein-Gordon field, the Yang-Mills field, and the Navier-Stokes equations. These models are used to describe phenomena such as particle interactions, fluid flow, and electromagnetic fields.

4. Are there any limitations to these models?

Like any scientific model, classical field models with infinite conserved quantities have their limitations. They are based on simplifying assumptions and may not accurately describe highly complex systems. Additionally, these models do not take into account quantum effects and may break down at very small length scales.

5. How are these models tested and validated?

Classical field models with infinite conserved quantities are tested and validated through a combination of theoretical calculations and experimental data. Scientists use mathematical techniques to make predictions based on these models, and then compare them to real-world observations. If the predictions match the data, it provides evidence for the validity of the model.

Similar threads

I Is Information a conserved quantity or not?
    • Classical Physics
Replies
3
Views
1K
I Spring balance analysis from a system point of view
    • Classical Physics
Replies
24
Views
727
A Were there any valid classical unified field theories ?
    • Classical Physics
Replies
4
Views
1K
I Some classical models of particles and quantum gauge theories
    • Quantum Interpretations and Foundations
Replies
0
Views
1K
I Is conservation of energy a local law in Quantum field theory?
    • Quantum Physics
Replies
18
Views
607
I Stern-Gerlach experiment with a classical object
    • Classical Physics
Replies
2
Views
680
Using Noether's Theorem to get conserved quantities
    • Advanced Physics Homework Help
Replies
2
Views
2K
I Atmospheric Density vs Altitude in an O'Neil Cylinder
    • Classical Physics
Replies
1
Views
588
Trick for conserved currents in classical field theory
    • Advanced Physics Homework Help
Replies
1
Views
954
A Importance of Densities in QFT
    • Quantum Physics
Replies
1
Views
797

Hot Threads

Recent Insights

Back
Top