All Questions
Tagged with symmetry-breaking field-theory
61
questions
3
votes
2
answers
579
views
What physical situation will give a negative mass squared?
Consider the Lagrangian density of $\phi^4$ theory
$$\mathcal{L}=-\frac{1}{2}\partial^\mu\phi\partial_\mu\phi-\frac{1}{2}m^2\phi^2-\frac{1}{24}\lambda\phi^4$$
the potential energy term is given by
$$...
- 181
1
vote
1
answer
415
views
Spontaneous symmetry breaking - potential minima
In spontaneous symmetry breaking, you expand the Lagrangian around one of the potential minima and write down the Feynman rules using this new Lagrangian.
Will it make any difference to your Feynman ...
- 3,203
1
vote
1
answer
283
views
Unitary matrix of pionic fields and pions as coordinate vectors
I am currently studding theory for Chiral Perturbation Theory( ChPT) and I have stumbled at two point, having a difficulty at understanding. I will present the problem at first and then phrase the ...
- 1,564
1
vote
4
answers
450
views
Lagrangian and finding equations of motion
I am given the following lagrangian:
$L=-\frac{1}{2}\phi\Box\phi\color{red}{ +} \frac{1}{2}m^2\phi^2-\frac{\lambda}{4!}\phi^4$
and the questions asks:
How many constants c can you find for which $\...
- 385
13
votes
3
answers
483
views
Why is imposing a symmetry on a theory considered more "natural" than fine-tuning its couplings?
Theories whose behavior would qualitatively change if their couplings were not fine-tuned to particular values are often dismissed as "unnatural" (in high-energy physics) or "unrealistic" (in ...
- 48.3k
3
votes
1
answer
685
views
Can charged scalar have non-zero vev?
In Higgs-Kibble mechanism, if we consider a $SU(2)_L$ doublet of complex scalar fields, then one of them is charged and the other neutral. Why does the neutral field acquire vev and not the charged ...
- 31
3
votes
2
answers
439
views
Determination of the ground state of a field theory
Consider the Spontaneous symmetry breaking in the theory
$$\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{\mu^2}{2}\phi^2+\frac{\lambda}{4!}\phi^4.$$
By the ground state of a classical ...
- 26.7k
2
votes
1
answer
213
views
Poincare non-invariance in real world and field theory
This may be a very blunt question but I wonder why we always use Poincare invariant Lagrangians in field theory. After all, the entire world around us is by no means homogeneous, isotropic and so on. ...
- 26.7k
4
votes
1
answer
582
views
Why should Ward identities only be used with the effective action (as opposed to the generating functional for connected diagrams)?
My question is about the derivation of Ward identities. I will sketch it here in the case of an O(N) symmetric model and point out what it bothering me when I am done. I am being very sloppy with the ...
- 4,375
9
votes
1
answer
712
views
effect of a simultaneous local and a global $U(1)$ symmetry breaking
EDIT : I am trying to figure out the effect of symmetry breaking in a $U(1)_Y\times U(1)_Z$ invariant lagrangian where $U(1)_Y$ is local symmetry of the Lagrangian and $U(1)_Z$ is a global symmetry of ...
- 26.7k
3
votes
1
answer
94
views
How does the choice of a particular vacuum in a field theory problem decide the number of Goldstone bosons?
How does the field expansion method (by this I mean expanding your fields about a chosen VEV and plugging into a given potential so that the masses of the fields are given by the coefficients in front)...
- 135
6
votes
1
answer
673
views
Spontaneous Symmetry Breaking
In Spontaneous symmetry breaking we have got that, a field $$\phi= \pm \sqrt{\frac{-m^2}{\lambda}}.$$ Now in order to get the unstable minima we need to guess the mass $m^2 <0 $. But can mass be ...
- 87
4
votes
1
answer
582
views
How is domain wall formation related to spontaneous symmetry breaking?
It is said that domain wall formation is the signature of in spontaneous symmetry breaking but not explicit symmetry breaking. Why is this so?
- 26.7k
2
votes
0
answers
178
views
Global part of a local symmetry?
What is exactly meant by "Global part of a Local symmetry"?
What are its implications on a field theory at classical level?
What are its implications at quantum level?
How is it related to symmetry ...
- 806
-1
votes
1
answer
280
views
Symmetry breaking with Lagrangian
I have been studying the spontaneous symmetry braking from Zee (Quantum Field theory ) and found in the page 224, he wrote the lagrangian as
$$\mathcal{L}=
\frac{1}{2}\{
λ
(∂φ)^2 + μ^2φ^ 2\} − \frac{\...
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