All Questions
Tagged with symmetry-breaking lagrangian-formalism
52
questions
4
votes
1
answer
254
views
Goldstone theorem in Schwartz
On page 566, Schwartz’s QFT book, to see the $\pi$ is the Goldstone boson, it reads:
$$J^\mu=\frac{\partial L}{\partial(\partial_\mu \pi)} \frac{\delta \pi}{\delta \theta}=F_\pi \partial_\mu \pi \tag{...
- 483
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0
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158
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When the EM vector field is given a mass by Higgs mechanism, why isn't this equivalent to a massive photon?
In chapter 6 of Classical Theory of Gauge Fields (Rubakov), we are presented with a scalar field $\phi$ coupled to the electromagnetic vector potential $A_\mu$. In this Lagrangian there is a quartic ...
- 9
1
vote
1
answer
969
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Two questions about Goldstone bosons
Let's say we are considering the case of Abelian symmetry, with the Lagrange density given by:
$$\mathcal{L}=\frac{1}{2}(\partial_\lambda \sigma)^2 + \frac{1}{2} (\partial_\lambda \pi)^2-V(\sigma^2 +\...
- 789
1
vote
0
answers
258
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Anderson-Higgs Mechanism
Consider an abelian gauge field coupled with a complex field:
$$\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+(D\varphi)^\dagger D\varphi+\mu^2 \varphi^\dagger\varphi-\lambda(\varphi^\dagger\varphi)^2.$...
- 131
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votes
0
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269
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Unitary gauge for spontaneous symmetry breaking
I'm given a lagrangian $$ \mathcal{L} = \partial_{\mu} \Phi^{\dagger} \partial^{\mu} \Phi + m^2 \Phi^{\dagger} \Phi - \lambda (\Phi^{\dagger} \Phi)^2 $$ where $m^2 > 0, \lambda > 0$. This ...
- 701
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votes
2
answers
663
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What is spontaneous in spontaneous symmetry breaking
When we say spontaneous symmetry breaking what do we mean by "spontaneous"?
The dictionary, for a non native speaker, relates it to the absence of an external stimulus.
In QFT and SM it simply says ...
user56963
1
vote
1
answer
84
views
Can we modify the Standard Model to fully break $SU(2)_L \times U(1)_Y$ symmetry?
I'm trying to understand how to see if a gauge symmetry would be fully or partially broken on Higgsing. Specifically I am looking at Lagrangians of the form
$$
\mathcal L = - \frac{1}{4} {F_a}_{\mu \...
- 1,212
2
votes
0
answers
153
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Breaking of supersymmetric QED in the O'Raifeartaigh model
The action for supersymmetric QED is
\begin{align}
S_{\text{SQED}} = \int d^4x\left\{8d(x)^2- F_{\mu\nu}(x)F^{\mu\nu}(x) - 4i\lambda(x)\sigma^{\mu}\partial_{\mu}\bar{\lambda}(x)+ |F_L(x)|^2 + |F_{\...
- 165
14
votes
1
answer
714
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What is "broken symmetry"?
For reference, I come from a mathematics background (mostly differential geometry). I have a very limited understanding of upper-level physics (I'm currently trying to fix this).
This is my current ...
- 467
1
vote
1
answer
417
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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
0
votes
1
answer
97
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Elecric field equations of motion
I'm reading this paper Quantum Time Crystals, Frank Wilczek, Center for Theoretical Physics, about time crystals, and in the situation described there is a particle of unit mass and charge $q$, ...
- 1,407
1
vote
4
answers
450
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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
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votes
3
answers
1k
views
Why do we need $SU(2)\times U(1)$ invariant mass terms if the symmetry will be broken anyway?
In the SM we can not add fermionic mass terms like $m \overline{e}_R e_L$ to the Lagrangian since these terms are not invariant under $SU(2)\times U(1)_Y$.
After introducing the Higgs in the unitary ...
- 1,230
-1
votes
1
answer
281
views
Understanding standard model and symmetry
I just want to know whether my understanding regarding standard model and symmetry is correct or utter nonsense.
The standard model is the (yet incomplete) Lagrangian of the
universe.
The Lagrangian ...
- 101
5
votes
2
answers
1k
views
What is classical Lagrangian? The Bare one or renormalized one? Are counterterms quantum corrections to renormalized Larangian?
EDIT
When one talks about the “classical Lagrangian” of a field, does one mean the renormalized Lagrangian with physical/renormalized masses and physical/renormalized couplings and without ...
- 26.8k
9
votes
2
answers
488
views
Quantum Anomalies and Quantum Symmetries
In Quantum Field Theories (QFT) there is a well known phenomenon of anomalies, where a classical symmetry is broken in the quantum theory due to a so called anomaly. This symmetry breaking can be ...
- 165
3
votes
2
answers
439
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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 ...
- 26.8k
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. ...
- 26.8k
5
votes
1
answer
805
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Why do we need spontaneous symmetry breaking in Lagrangian formalism?
I have always struggled with the concept of spontaneous symmetry breaking. It seems to me that many others don't find it very intuitive as well, but that could be just me having difficulties with the ...
- 844
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1
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282
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How does one prove that the current of a spontaneously broken symmetry generates a particle?
I am having a hard time arguing that, after spontaneous breaking of a continuous symmetry of a field Lagrangian, local fluctuations around the vacuum can be interpreted as particles (without referring ...
- 211
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votes
1
answer
1k
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What to do with a $\phi$ term in a Lagrangian?
I am considering a Lagrangian that is of the following form:
$$\mathcal{L}=-{1\over 2}\partial_\mu\phi\partial^\mu\phi+2\mu^2\phi^2+2\sqrt{6}{\mu^3\over \lambda}\phi + {9\mu^4\over 2\lambda} + \text{...
- 16.4k
5
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1
answer
927
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Spontaneous symmetry breaking and 't Hooft and Polyakov monopoles
What is spontaneous symmetry breaking from a classical point of view. Could you give some examples, using classical systems.I am studying about the 't Hooft and Polyakov magnetic monopoles solutions, ...
user7757