Loading [MathJax]/extensions/TeX/AMSsymbols.js
Jump to content

Recommended Posts

Posted

This is spontaneous symmetry breaking rather than explicit symmetry breaking. The Lagrangian respects all the symmetries in question, but the vacuum state does not.

Posted

Which terms exactly are related to Symmetry breaking?! ajb?!

 

The vacuum expectation value of the Higgs field.

Posted

Thanks ajb for the advice. I already have the equation. I was just searching for further information. I do know the equivalent unification.

 

Best Thanks.

Posted

Ryder explains spontaneous symmetry breaking in this book [1]. Just about any book on QFT and particle physics will say something.

 

 

References

 

[1] L. Ryder. "Quantum Field Theory", Cambridge University Press; 2 edition (June 13, 1996).

Posted

No problem. Ryder presents two nice analogies, one mechanical and the other from statistical mechanics. The essential feature of spontaneous symmetry breaking is a degenerate vacuum. The Lagrangian or Hamiltonian describing the system remains invariant under the symmetry in question, the physical system is not invariant as one of the vacua has to be chosen.

Posted

And, the degeneracy comes out in the solution of the Lagrangian. What do you think ajb?

 

Yes, in the vacuum solution in particular.

Posted

By the way ajb, many field theories are solved by the Lagrangian and an Equivalent Formula. I think the Lagrangian is very difficult.

Posted

Quite generally the Lagrangian approach works well, especially when quantisation is required. However, one can have theories that are not governed by a Lagrangian and those whose Hamiltonian formalism is not equivalent.

Posted

AJB ...... For the equivalent Hamiltonian Model; I have The Perturbed Dirac's Model ..... have written (down) it since years.

 

[latex]H_{ew}=H_{Dirac}+H_{zo}+H_{w+}+H_{w-}+LT[/latex]

 

Do you have any idea, about this?

Posted

Gauge theories are quite complicated to deal with in the Hamiltonian formalism. Technically we have constraints to deal with, but this can be done.

 

Most particle theorists like to use path integrals and this is best formulated in terms of a Lagrangian.

Posted

But, you will have to apply LAP on the Lagrangian which is very complicated, especially when the Lagrangian is long and unabbreviatable. Are there sufficient approximations and neglectance in Electroweak?

Or, there is simpler manipulation.

 

[Latex] H_{w+}=1/2W^{ij}_{t}W^{k}_{ij} epsi^{t}[/Latex]

Could you confirm, AJB?

Posted

But, you will have to apply LAP on the Lagrangian which is very complicated, especially when the Lagrangian is long and unabbreviatable.

 

What is LAP?

 

[Latex] H_{w+}=1/2W^{ij}_{t}W^{k}_{ij} epsi^{t}[/Latex]

Could you confirm, AJB?

 

I am not really familiar with the Hamiltonian formulation of the electroweak theory. All the references I have use path integrals in the Lagrangian formulation.

Posted

LAP: Least Action Principle.

 

Ok, so you use this to get at the classical equations of motion. These are important in quantum field theory, but as I am sure you now the path integral approach takes into account all configurations.

Posted (edited)

Do you mean that we integrate on path, or on (Z,W+,W-) - variable path?

I do know that this is said to have relation with Feynman-Diagrams Likes.

Edited by Amr Morsi

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.