Gauge symmetry and symmetry breaking

In summary, the gauge symmetry in a theory is still present after symmetry breaking, but may not be manifest due to the perturbative solution breaking it down to a subgroup. The relevance of this symmetry can also be affected by the choice of effective field theory and any present anomalies. In the case of scalar electrodynamics, the question of whether the effective potential depends on a certain variable may lead to questioning the manifestness of the gauge symmetry after symmetry breaking.
  • #1
touqra
287
0
How would one know in general, whether an original gauge symmetry in the theory is still gauge symmetrical after symmetry breaking? I mean is there a theorem or something like that?
And the other way around, is there a general way of knowing whether there is the possibility of a hidden, i.e. not manifest gauge symmetry from a theory?
 
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  • #2
Yes the gauge symmetry is still there in the full theory, its just not manifest anymore b/c the perturbative solution has broken the original symmetry down to a subgroup.

From the point of view of effective field theory with some set cutoffs, its no longer relevant.

The only way a gauge symmetry can dissappear in quantum field theory, is if there is an anomaly present. Those sorts of theories are generally believed to be inconsistent.
 
  • #3
Haelfix said:
Yes the gauge symmetry is still there in the full theory, its just not manifest anymore b/c the perturbative solution has broken the original symmetry down to a subgroup.

From the point of view of effective field theory with some set cutoffs, its no longer relevant.

The only way a gauge symmetry can dissappear in quantum field theory, is if there is an anomaly present. Those sorts of theories are generally believed to be inconsistent.

That's what I was thinking. I was doing scalar electrodynamics after symmetry breaking, adding the ghost term and the [tex]R_{\xi}[/tex] gauge, computing the one-loop correction to the effective potential.

The question asked to show that to one-loop correction, the effective potential does not depend on [tex]\xi[/tex]. But my corrections failed to cancel half of the terms with [tex]\xi[/tex].
That's how this question I posted came into my mind. Perhaps the question was wrong, and indeed the gauge symmetry is no longer manifest after symmetry breaking. Hence, it does depend on [tex]\xi[/tex].
 

1. What is gauge symmetry?

Gauge symmetry is a fundamental concept in physics that refers to the invariance of a physical theory under a certain transformation. In other words, it is the property of a theory that remains unchanged even when certain variables or parameters are transformed. This is important in understanding the fundamental forces of nature, such as electromagnetism and the strong and weak nuclear forces.

2. What is symmetry breaking?

Symmetry breaking is a phenomenon in which a system that exhibits symmetry at a certain level becomes asymmetric at a lower level. In the context of gauge symmetry, it refers to the breaking of the symmetry between particles and forces, resulting in the emergence of different masses and interactions. This is a crucial concept in the Standard Model of particle physics.

3. How does gauge symmetry play a role in the Standard Model?

Gauge symmetry is a fundamental principle in the Standard Model that explains the interactions between matter particles (such as quarks and leptons) and force particles (such as photons and gluons). It allows for the unification of the electromagnetic, weak, and strong forces into one theoretical framework. The breaking of gauge symmetry is also responsible for the generation of mass for particles.

4. What is the Higgs mechanism and how does it relate to gauge symmetry?

The Higgs mechanism is a theoretical concept that explains the origin of mass in particles. It is closely related to gauge symmetry as it involves the breaking of the symmetry between particles and forces. According to the Higgs mechanism, particles acquire mass through interactions with the Higgs field, which is a field that permeates the entire universe and gives rise to the Higgs boson particle.

5. How does gauge symmetry and symmetry breaking relate to the search for a unified theory of physics?

The search for a unified theory of physics, also known as a theory of everything, is closely linked to gauge symmetry and symmetry breaking. This is because such a theory would need to explain how all the fundamental forces of nature are related and unified. Gauge symmetry and symmetry breaking play an essential role in this unification, as they provide a framework for understanding the interactions between particles and forces at a fundamental level.

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