What is the concept of scale invariance in quantum field theory?

In summary, the conversation discusses Howard Georgi's concept of Unparticle Physics and its basis in the principle of scale invariance. He suggests the possibility of another sector of the theory that interacts weakly with the standard model and is exactly scale-invariant. Georgi explains that a free massless particle is an example of scale-invariant stuff, but there are more interesting possibilities in quantum field theory where fields can scale with fractional dimensions. The conversation ends with a question about the meaning of scale invariance in quantum field theory and Georgi's suggestion of fields scaling with fractional dimensions being related to dimensional regularization for renormalization.
  • #1
beyondthemaths
17
0
Hey guys!

I was reading the following paper http://arxiv.org/abs/hep-ph/0703260 for Georgi and I have a conceptual question about it.

Howard Georgi was talking about this Unparticle Physics theory and at the base of his analysis is the principle of scale invariance. So Georgi is saying what if there were another sector of the theory that interacts so weakly with the standard model that it hasn’t been noticed yet, and what if it were exactly scale-invariant?

He then mentions: "A free massless particle is a simple example of scale invariant stuff because the zero mass is unaffected by rescaling. But quantum field theorists have long realized that there are more interesting possibilities — theories in which there are fields that get multiplied by fractional powers of the rescaling parameter."

He adds: "It is clear what scale invariance is in the quantum field theory. Fields can scale with fractional dimensions."

My question now is: What does he mean by that last sentence in bold? What is [scale invariance](http://en.wikipedia.org/wiki/Scale_invariance) in quantum field theory? Now I can say in QFT when electromagnetic field is quantized, there the photon has zero mass and is thus scale invariant. But he is pointing to something else "more interesting" as he said so what is that? And finally what does he mean by "fields can scale with fractional dimensions?"
 
Physics news on Phys.org
  • #2
I think he just means that one can perform dimensional regularisation for renormalisation, no?
 

1. What is scale invariance and how does it relate to quantum field theory (QFT)?

Scale invariance is a property of a physical system where the laws governing its behavior remain unchanged under a change in scale. In the context of QFT, this means that the equations and predictions of the theory hold true regardless of the size or energy of the system being studied. This is important in understanding the behavior of particles at different energy levels and in different regions of space.

2. How is scale invariance broken in QFT?

Despite the fundamental nature of scale invariance in QFT, it is often broken in realistic models due to various factors such as quantum corrections, interactions between particles, and the presence of external fields. These effects can lead to a violation of scale invariance and result in important physical consequences, such as the emergence of mass and the hierarchy problem.

3. What is the role of renormalization in maintaining scale invariance in QFT?

Renormalization is a powerful tool in QFT that allows us to remove divergences and inconsistencies in calculations, which arise due to the breakdown of scale invariance. By taking into account the effects of all energy scales, renormalization enables us to make accurate predictions and maintain the underlying symmetry of scale invariance.

4. Can scale invariance be used to explain the behavior of systems at extreme energy scales, such as the early universe?

Yes, scale invariance plays a crucial role in understanding the behavior of systems at extreme energy scales, such as in the early universe. The principles of scale invariance allow us to extrapolate from the behavior of particles at low energies to high energies, providing insights into the behavior of the universe in its earliest stages.

5. How does the concept of conformal symmetry relate to scale invariance in QFT?

Conformal symmetry is a more specific type of symmetry that is closely related to scale invariance. In addition to preserving the laws of physics under a change in scale, conformal transformations also preserve the angles between particles. This symmetry is particularly important in the study of conformal field theories, which are theories that exhibit both scale invariance and conformal symmetry.

Similar threads

  • High Energy, Nuclear, Particle Physics
Replies
2
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
7
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
6
Views
2K
  • Quantum Physics
Replies
1
Views
737
  • Quantum Interpretations and Foundations
3
Replies
91
Views
5K
  • Beyond the Standard Models
Replies
7
Views
2K
  • Quantum Interpretations and Foundations
11
Replies
370
Views
9K
  • High Energy, Nuclear, Particle Physics
Replies
2
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
7
Views
2K
Back
Top