Amr Morsi Posted July 12, 2011 Posted July 12, 2011 When the Symmetry gets broken, how the Lagrangian gets affected in the Electroweak Force?
ajb Posted July 12, 2011 Posted July 12, 2011 This is spontaneous symmetry breaking rather than explicit symmetry breaking. The Lagrangian respects all the symmetries in question, but the vacuum state does not.
Amr Morsi Posted July 14, 2011 Author Posted July 14, 2011 Which terms exactly are related to Symmetry breaking?! ajb?!
ajb Posted July 14, 2011 Posted July 14, 2011 Which terms exactly are related to Symmetry breaking?! ajb?! The vacuum expectation value of the Higgs field.
Amr Morsi Posted July 21, 2011 Author Posted July 21, 2011 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.
ajb Posted July 21, 2011 Posted July 21, 2011 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).
ajb Posted July 22, 2011 Posted July 22, 2011 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. 1
Amr Morsi Posted July 23, 2011 Author Posted July 23, 2011 And, the degeneracy comes out in the solution of the Lagrangian. What do you think ajb?
ajb Posted July 23, 2011 Posted July 23, 2011 And, the degeneracy comes out in the solution of the Lagrangian. What do you think ajb? Yes, in the vacuum solution in particular.
Amr Morsi Posted July 23, 2011 Author Posted July 23, 2011 By the way ajb, many field theories are solved by the Lagrangian and an Equivalent Formula. I think the Lagrangian is very difficult.
ajb Posted July 24, 2011 Posted July 24, 2011 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.
Zarnaxus Posted July 30, 2011 Posted July 30, 2011 http://www2.b3ta.com/host/creative/39226/1271285612/pimpmystandardmodel.png
ajb Posted July 30, 2011 Posted July 30, 2011 http://www2.b3ta.com/host/creative/39226/1271285612/pimpmystandardmodel.png yes, so the Higgs is really "bolted on to" the standard model to give us massive gauge bosons while keeping renormalisation. In this sense it is probably the ugliest part of the standard model.
Amr Morsi Posted July 31, 2011 Author Posted July 31, 2011 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? 1
ajb Posted July 31, 2011 Posted July 31, 2011 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.
Amr Morsi Posted July 31, 2011 Author Posted July 31, 2011 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? 1
ajb Posted July 31, 2011 Posted July 31, 2011 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.
ajb Posted July 31, 2011 Posted July 31, 2011 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.
Amr Morsi Posted August 1, 2011 Author Posted August 1, 2011 (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 August 1, 2011 by Amr Morsi
Amr Morsi Posted August 1, 2011 Author Posted August 1, 2011 [latex]W^{ij}_{k}=alpha*m*Wepsi^{i}_{,j}*kdelta^{i}_{k}[/latex] Is the previous true?
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