All Questions
Tagged with symmetry-breaking lagrangian-formalism
52
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Unitary Gauge Removing Goldstone Bosons
The Lagrangian in a spontaneously broken gauge theory at low energies looks like
$$ \frac{1}{2} m^2 ( \partial_\mu \theta - A_\mu )^2 $$
and the gauge transformations look like $\theta \rightarrow \...
- 29
6
votes
1
answer
148
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Goldstone theorem for classical and quantum potential
Consider a quantum theory $$\mathcal{L}(\phi^a) = \mathcal{L_{kin}}(\phi^a)-V(\phi^a),\tag{11.10}$$ depending on any type of fields $\phi^a$.
The VEV of this theory are constant fields $\phi_0^a$ such ...
- 305
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Calculation of Vertex factor from Lagrangian
I am studying spontaneous symmetry breaking of a complex scalar field $\phi(x)$ of a global $U(1)$ symmetry: $\phi(x)\to e^{i\alpha}\phi(x)$, where $\alpha$ is a real constant. I am considering the ...
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Residual Symmetry Group after Spontaneous Symmetry Breaking
I am seeking a proof of the following:
Suppose we have a theory with $n$ scalar fields $(\phi_1,...,\phi_n)$ such that the Lagrangian $L$ is invariant under the action of some group $G$.
However, $G$ ...
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1
answer
141
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$SU(2)$ breakdown to $U(1)$
When we break a lagrangian symmetric with $SU(2)$ with a higgs bosons being the adjoint representation, using the following v.e.v for higgs $\phi$,
$$\langle \phi \rangle = (0,0, \rho)^T.$$
Two ...
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1
vote
1
answer
210
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Symmetry groups breaking for the lagrangian of two complex scalar fields
Suppose we have a generic non-interacting Lagrangian of two complex scalar fields,
\begin{align}
\mathcal{L} &= (\partial^\mu \Phi^\dagger)(\partial_\mu \Phi) - \Phi^\dagger\mathbb{M}^2\Phi \tag{1}...
- 1,783
1
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1
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73
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What is the reverse operation of gauging a global symmetry?
As far as I understand, gauging a global symmetry means taking a model with a global symmetry and transforming it into a model such that the previous symmetry group is now the gauge symmetry of your ...
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1
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Do we have an analytic calculation to derive $\frac{F^2}{4}\,\text{Tr}\left\{\partial_\mu U\partial^\mu U^{\dagger}\right\}$ from the QCD Lagrangian?
I have studied the quark condensate and chiral perturbation theory. However, I am not sure where the "kinetic term" of the pion
$$\frac{F^2}{4}\operatorname{Tr}\left\{\partial_\mu U\partial^...
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2
votes
1
answer
102
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In QFT, are there any restrictions on spontaneous breaking $G\to H$, due to "spontaneity"?
For simplicity, let us restrict to the spontaneous breaking of global symmetries. Given any pair of groups $G\supset H$, is it always possible to find a $G$-invariant Lagrangian that gives a QFT such ...
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Decoupling in the Linear Sigma Model
In Schwartz's 'QFT and The Standard Model' the Lagrangian for the linear sigma model is given by:
$$L=\frac{1}{2}(\partial_\mu\sigma)^2+(\sqrt\frac{2m^2}{\lambda}+\frac{1}{\sqrt 2}\sigma(x))^2\frac{1}{...
- 199
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Quantization of spontaneously broken theory, which is not in the true vacuum
I wonder whether the source $J$ in QFT can make one to quantize the field when the system is in the excursion to the minimum. Precisely, I want to know that following process makes sence.
Suppose, I ...
- 13
3
votes
1
answer
219
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How can we determine which subgroup remains unbroken after spontaneous symmetry breaking for $SU(2)\times U(1)$ symmetry?
Consider an $SU(2)$ doublet of bosons $\Phi = (\phi^+, \phi^0)^T$, where the complex scalar field $\phi^+$ destroys positively charged particles and creates negatively charged ones, and the complex ...
- 1,783
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333
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Peskin and Schroeder, Linear sigma model, renormalized perturbation theory
On Peskin & Schroeder's QFT pages 353-355, the book uses the Linear sigma model to illustrate the renormalization and symmetry.
We can write the Lagrangian of Linear sigma model with
$$
\begin{...
- 1,421
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169
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Taylor expansion of some Lagrangian (Understanding the Blundell's Quantum field theory, Example 26.5)
I am reading the Lancaster, Blundell's Quantum field theory for the Gifted Amateur, p.243, Example 26.5 and I can't understand some sentences and I don't know how to expand some Lagrangian.
I am a ...
- 327
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Can Chiral symmetry violating term in lagrangian violate charge conversation?
The regular Lagrangian is
$\mathcal{L}=\bar{\psi}(i\gamma^\mu\partial_\mu-m)\psi$
If we add a chiral violating term
$\mathcal{L}=\bar{\psi}(i\gamma^\mu\partial_\mu-me^{i\theta\gamma^5})\psi$
For the ...
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