# Observables when the symmetry is not broken?

• A
• mbond
In summary, it is possible to observe the quantum of the field in the case where the symmetry is not broken, but it is not possible in the case of inflationary cosmology.
mbond
Hi,

Let be a scalar field φ that permeates all space. The quantum of the field has a mass m. The field is at the minimum of its potential. When this minimum is for φ≠0 (a broken symmetry), the quantum may be observed by exciting the field, as with the Higgs boson.

But if the symmetry is not broken, the field is at the minimum of its potential for φ=0. Is it then possible to observe its quantum?

I am asking this thinking of inflationary cosmology: in a scenario such as the "new inflation" the inflaton field potential has its minimum for φ≠0. The inflaton boson may then, at least in a thought experiment, be observable with an accelerator. But with the "chaotic inflation" the minimum is at φ=0. Is the inflaton boson observable then?

I would be grateful if you could enlighten me.

Last edited:
You are a bit vague. What symmetry are you talking about? Is the symmetry a global one or a local gauge symmetry.

If you have a global symmetry (like the light-quark sector of QCD in the chiral limit, which has a ##\mathrm{SU}(2)_{\text{L}} \times \mathrm{SU}(2)_{\text{R}}## chiral symmetry), then you can have symmetry breaking. Then some scalar or pseudoscalar field has a non-vanishing vacuum expectation value. In the case of QCD that's the non-vanishing scalar quark condenstae, ##\langle \Omega|\bar{\psi} \psi|\Omega \rangle \neq 0##. This breaks the chiral symmetry to ##\mathrm{SU}(2)_{\text{V}}## (that it's the iso-vector subgroup that's the unbroken part is due to the small different quark up- and down-quark masses).

In hadron phenomenology that implies that there are 3 massless pseudoscalar particles, which are the pions. In reality they have a (small) mass, because the chiral symmetry is only approximate and broken by the light-quark masses. The order parameter of the chiral symmetry, the quark condensate, maps to a corresponding scalar-boson state, the ##f_0(500)## aka ##\sigma##-meson.

Usually for each quantum field you also have the corresponding excitations which are observed as particles. There's no doubt about the pions. It's already somewhat difficult for the ##\sigma##-meson, which is a very broad resonance rather then anything resembling a particle.

I can't say anything about inflatons since I'm not familiar enough with the quantum aspects of inflation.

mbond said:
the quantum may be observed by exiting the space

What do you mean by this?

PeterDonis said:
What do you mean by this?
exciting, sorry.

mbond said:
exciting, sorry

Ok, but then "exciting the space" isn't correct. You don't excite the "space", you excite the field--you add energy to it, in order to observe quanta of the field.

## 1. What are observables in relation to symmetry?

Observables are physical quantities that can be measured or observed in a system. In the context of symmetry, observables are quantities that remain unchanged when a system undergoes a symmetry transformation.

## 2. What happens to observables when symmetry is not broken?

When symmetry is not broken, observables remain unchanged under symmetry transformations. This means that the values of observables will be the same before and after the transformation.

## 3. Can observables change if symmetry is not broken?

No, observables cannot change if symmetry is not broken. This is because symmetry transformations preserve the values of observables.

## 4. How do observables behave when symmetry is not broken?

When symmetry is not broken, observables behave in a predictable manner. They will have the same values before and after symmetry transformations, and their behavior will be consistent with the underlying symmetry of the system.

## 5. What is the significance of observables in systems with unbroken symmetry?

Observables play a crucial role in understanding systems with unbroken symmetry. They provide a way to measure and describe the behavior of the system, and their preservation under symmetry transformations can reveal important information about the underlying symmetry and dynamics of the system.

• Beyond the Standard Models
Replies
1
Views
784
• Cosmology
Replies
6
Views
1K
• Quantum Physics
Replies
3
Views
968
• High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
• Quantum Physics
Replies
87
Views
5K
• Quantum Physics
Replies
2
Views
4K
• Cosmology
Replies
3
Views
2K
• Cosmology
Replies
1
Views
1K
• Cosmology
Replies
7
Views
3K
• Advanced Physics Homework Help
Replies
1
Views
940