Scaling and the renormalization (sub)group

In summary, the renormalization (sub)group ideas are mainly applied in particle physics and equilibrium critical behaviour. Other fields where it can be applied include fluid mechanics, although further research is needed in this area. When cosmologists refer to the 'electroweak phase transition', they are essentially talking about the change in Higg's field vacuum expectation value and the spontaneous breaking of its symmetry.
  • #1
Carlos L. Janer
114
3
I am aware of only two fields where the renormalization (sub)group ideas can be systematically and
unambiguously applied: particle physics and equilibrium critical behaviour.

1.- Are there any others?

2.- What are these ideas used for in fluid mechanics?

3.- When cosmologists speak about 'electroweak phase transition' what do they really mean? Is it just the fact
that Higg's field vacuum expectation value changed to a non null value and its symmetry was spontaneously
broken?

I am not quite sure where I should be posting this.
 
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  • #2
1. There are general symmetry methods for differential equations which include scaling transformations to find first integrals. See e.g. Olver's "Application of Lie Groups to Differential Equations".

2. I've not worked enough in the area of fluid mechanics to answer.

3. I believe that's exactly it.
 

1. What is scaling and why is it important in physics?

Scaling refers to the behavior of a physical system when its size or parameters are changed. It is important in physics because it allows us to understand how a system behaves at different scales, which is crucial for studying complex systems and predicting their behavior.

2. How does the renormalization group relate to scaling?

The renormalization group is a mathematical framework used to study scaling behavior in physical systems. It allows us to understand how a system's properties change as we zoom in or out on different length or energy scales.

3. What is the significance of the renormalization group in quantum field theory?

The renormalization group is essential in quantum field theory because it helps us deal with the divergences that arise in calculations. It allows us to extract meaningful physical predictions from these calculations by accounting for the effects of different energy scales.

4. Can you give an example of how scaling and the renormalization group are applied in real-world situations?

One example is in critical phenomena, where physical systems undergo a phase transition at a critical point. The renormalization group allows us to study how the system's properties change as we approach this critical point, providing insight into the system's behavior at different length scales.

5. What is the relationship between renormalization and the renormalization group?

Renormalization is a technique used to remove infinities from calculations in quantum field theory. The renormalization group is a more general framework that extends this technique to study scaling behavior in a wider range of physical systems, not just in quantum field theory.

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