Gauge invariance and it's relation to gauge bosons

In summary: For abelian gauge theory you can think of the mass term as a remnant of a more general non-abelian symmetry -> spontaneous symmetry breaking.In summary, the question posed by the supervisor is about why gauge invariance forbids mass terms for gauge bosons. This difficulty can be avoided through the Higgs mechanism, which preserves gauge invariance and renormalizability. The book "Quantum Field Theory" by Mark Srednicki discusses this topic in chapters 54, 58, and 69. Additionally, the concept of a mass term being a remnant of a more general non-abelian symmetry is also mentioned.
  • #1
PsiPhi
20
0
Hello,
I'm currently doing a project that is concerned with the hopeful discovery of the Higgs Boson at LHC. I'll be running some code that my supervisor has produced, but before that he wanted me to understand more of the physics that is behind the Higgs mechanism.

He has proposed a question to me, "Why gauge invariance forbids mass terms for gauge bosons?"

I've been reading quite a few textbooks and I'm not too sure if this could be the answer to the problem. The answer had an explanation from the Bose-Einstein condensate (BEC) context, where it talks about definite phase of the complex wavefunction describing the BEC and the existence of such a phase breaks global gauge invariance - a symmetry associated with particle conservation.
Could this particle conservation be the reason for no mass terms in gauge invariance? Another possible answer could be a chapter I read on about the Goldstone boson.

I have a feeling that the two possible explanations that I've provided for the question are way off the mark.

Could anyone recommend a textbook, particular topics about the question or websites that may shed some light on my question?

Cheers.
 
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  • #2
PsiPhi said:
"Why gauge invariance forbids mass terms for gauge bosons?"

fermion mass terms in the lagrangian [tex]m\bar{\psi}\psi[/tex] are scalar. Maybe you should try to rewrite this term as a function of [tex]\psi_L[/tex] and [tex]\psi_R[/tex] ?
 
  • #3
The reason why a by-hand mass term is forbidden in a gauge theory is that this spoils gauge invariance and the theory loses renormalizability. These are two fundamental ingredients for the proper working of the theory. This difficulty can be evaded through the Higgs mechanism. The proof that a gauge theory with the Higgs mechanism is renormalizable is due to Veltman and 't Hooft as I think you know.

Cheers

Jon
 
  • #4
PsiPhi said:
"Why gauge invariance forbids mass terms for gauge bosons?"
Read chapers: 54, 58 and 69. of this book -> http://www.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf
In chapters 58 and 69 it is explicitly stated that theory with mass term in Lagrangian don't forbid gauge invariance!
 
  • #5
QuantumDevil said:
Read chapers: 54, 58 and 69. of this book -> http://www.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf
In chapters 58 and 69 it is explicitly stated that theory with mass term in Lagrangian don't forbid gauge invariance!

Where do you see it ?
 
  • #6
Page 346 below equation 58.7
 
  • #7
okey, you're right it's my mistake. His question was about mass term for gauge bosons not matter fields.
 

1. What is gauge invariance?

Gauge invariance is a fundamental principle in physics that states that the physical laws governing a system should be independent of the choice of gauge, or mathematical representation, used to describe it. This means that the equations used to describe a physical system should not change when the gauge is changed.

2. How does gauge invariance relate to gauge bosons?

Gauge invariance is closely related to gauge bosons, as these are the particles responsible for mediating interactions between particles in a gauge theory. Gauge bosons are considered gauge invariant as their interactions with other particles are not affected by a change in gauge.

3. What is the role of gauge bosons in gauge theories?

In gauge theories, gauge bosons are responsible for carrying the fundamental forces between particles. They are considered force carriers and are responsible for mediating the interactions between particles in a gauge theory, such as the strong and weak nuclear forces.

4. How do gauge bosons affect the behavior of particles?

Gauge bosons affect the behavior of particles by mediating the interactions between them. They carry the fundamental forces that govern the behavior of particles, such as the strong and weak nuclear forces, and their interactions can be described using gauge theories.

5. Can gauge invariance be broken?

Yes, gauge invariance can be broken in certain situations. This can occur through the Higgs mechanism, where a field called the Higgs field gives masses to certain gauge bosons, breaking the symmetry of the gauge theory. This is what gives particles their mass in the Standard Model of particle physics.

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