Asymptotic safety and local gauge invariance

In summary, the conversation discusses the topic of whether local gauge invariance is a requirement for a fundamental theory within quantum field theory (QFT) and if it is necessary for an asymptotically safe theory. The speaker mentions that they have found scattered remarks by F. Wilczek on the subject and is seeking good references or statements on the state of the topic. Another participant points out that gauge invariance is not a fundamental requirement for nonlinear relativistic QFT in all dimensions and provides a reference discussing rigourous constructions in 2 and 3 dimensions. However, it is noted that Yang-Mills, which is a gauge theory, seems to be the best candidate for a rigourous construction in 4 dimensions. The
  • #1
metroplex021
151
0
Hi folks -- does anyone know of a good survey article on the topic of whether local gauge invariance is a requirement of a fundamental theory within QFT -- hence of an asymptotically safe theory?

I only have a few scattered remarks to this effect (by F. Wilczek mostly), so any good references or even statements of the state of play would be most appreciated!
 
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  • #2
Gauge invariance is not a fundamental requirement for a nonlinear relativistic quantum field theory that rigourously exists, at least not in all dimensions. For example, http://www.claymath.org/sites/default/files/yangmills.pdf (section 6.2) says there are rigourous nonlinear scalar fields in 2 and 3 dimensions. However they go on to discuss that in 4 dimensions the best candidate for a rigourous construction seems to be Yang-Mills, which is a gauge theory.
 
  • #3
thank you very much, that is tremendously helpful!
 

Related to Asymptotic safety and local gauge invariance

1. What is asymptotic safety in relation to local gauge invariance?

Asymptotic safety refers to the property of a quantum field theory where the interactions between particles become weaker at high energies, allowing for a consistent and well-defined theory. Local gauge invariance, on the other hand, is a symmetry in which the laws of physics remain unchanged under local transformations. The combination of these two concepts leads to a theory that is both well-defined and consistent at all energy scales.

2. How does asymptotic safety differ from renormalizability?

While both asymptotic safety and renormalizability refer to the behavior of quantum field theories at high energies, they are not the same thing. Renormalizability refers to the ability to remove divergences in perturbative calculations, while asymptotic safety is a more general property that allows for a consistent theory at all energy scales.

3. What evidence supports the existence of asymptotic safety?

There is currently no direct experimental evidence for asymptotic safety. However, there is theoretical evidence from various approaches, such as the functional renormalization group, which suggest that asymptotic safety is a possible solution to the problem of non-renormalizability in quantum field theories.

4. Can asymptotic safety be applied to all quantum field theories?

No, not all quantum field theories are asymptotically safe. Theories that are asymptotically safe must have certain properties, such as a finite number of relevant couplings, which is not the case for all theories. Additionally, the existence of asymptotic safety is a subject of ongoing research and is not yet fully understood.

5. How does local gauge invariance relate to the Standard Model of particle physics?

Local gauge invariance is a fundamental principle in the Standard Model of particle physics. It is the symmetry that allows for the consistent interactions between particles and the unification of the electromagnetic, weak, and strong forces. Without local gauge invariance, the Standard Model would not be able to accurately describe the behavior of particles and their interactions.

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