All Questions
Tagged with quantum-electrodynamics lagrangian-formalism
72
questions
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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
0
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0
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68
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Feynman diagrams in Yukawa interaction
I want to understand drawing Feynman Diagrams better, therefore I wanted to draw some for the Lagrangian with a Yukawa interaction term:
$$L = \bar{\psi}(i \partial\!\!\!/ - m)\psi - g \bar{\psi}\phi \...
0
votes
1
answer
109
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Equations of motion for Lagrangian of scalar QED [closed]
I really would appreciate your help with this exercise.
I have the Lagrangian for scalar electrodynamics given by:
$$\mathcal{L}=-\frac{1}{4}F_{\mu\nu}(x)F^{\mu\nu}(x)+(D_\mu\varphi(x))^*(D^\mu\varphi(...
- 11
1
vote
1
answer
64
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Charge renormalization choice in QED
In the lectures on QFT I'm following we define the renormalized QED Lagrangian as
$$\mathcal{L} = \dfrac{1}{4} (F_0)_{\mu\nu} (F_0)^{\mu\nu} + \bar{\psi}_0 (i \bar{\partial} - (m_0)_e) \psi_0 - e_0 \...
- 1,613
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48
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Ward identity in scalar QED; gauge transformations & plane wave solutions for polarization
I am prepping for my QFT2 exam tomorrow, and in one of the mock exams I found the following question (and I'm not quite sure how to go about this). Given the following Lagrangian:
$$
L = -\frac{1}{4}...
2
votes
1
answer
94
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Why are these terms not present in the QED Lagrangian?
I am working though some questions for my QFT/ QED exam and i am having trouble with the following question:
Explain why the following terms cannot be part of the Lagrangian of QED:
$-g(\bar{\psi}\...
- 35
0
votes
1
answer
82
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Conserved current from a symmetry
Good morning. I was reading Tong's Quantum Field Theory course and got stuck on a somewhat stupid step. Essentially, considering the Lagrangian density
$$
L = - F_{\mu \nu}F^{\mu \nu} + i \bar{\psi} \...
- 161
2
votes
1
answer
154
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Deriving Feynman rules for scalar QED
I am a bit confused about Matthew D. Schwartz's statement of the Feynman rules in scalar QED (chapter 9, section 9.2 titled Feynman rules for scalar QED. The Lagrangian is
\begin{equation}
\mathcal{L} ...
- 904
1
vote
1
answer
218
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Fermion Propagator
Will the fermion propagator change if instead of deriving it from the Lagrangian
$$\mathcal{L}=i\bar{\Psi}\gamma^{\mu}\partial_{\mu}\Psi
-m\bar{\Psi}\Psi\tag{1}$$
I derive it from
$$\mathcal{L}'=\frac{...
- 3,992
1
vote
0
answers
115
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Is there an intuitive way to understand the Lagrangian for magnetic and electric dipole moment?
From the textbook I learned that the electric dipole moment (EDM) and magnetic dipole moment (MDM) has the following Lagrangian:
$$\mathcal{L}_{EDM}=F_{\nu\mu}\bar{\psi}\gamma^{5}\left[ \gamma^{\nu},\...
- 619
1
vote
2
answers
191
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Massless QED modified Lagrangian
Consider a massless theory of QED, with Lagrangian
$$\mathcal{L}_{QED}=
-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\bar{\Psi}i\gamma^{\mu}\partial_{\mu}\Psi+
e\bar{\Psi}\gamma^{\mu}A_{\mu}\Psi$$
Is there any ...
- 3,992
1
vote
0
answers
75
views
Scalar particle Compton scattering using relativistic Lagrangian formulation of electromagnetism
We know that parallel to scalar QED, a common formalism that describes a massive particle coupled to electromagnetism is through a relativistic worldline formalism, which writes
$$\mathcal{S}=\int\ ds\...
- 76
3
votes
2
answers
219
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A question on Schwartz's derivation of the Euler-Heisenberg Lagrangian
In Subsection 33.2.2. of Schwartz's Quantum Field Theory and the Standard Model, he starts to derive the Euler-Heisenberg effective Lagrangian by "replacing" the field which is being ...
- 1,254
1
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1
answer
124
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Why did Schwinger [Phys. Rev. 74 (1948) 1439] choose a non-standard form of the Lagrangian density associated with the free electromagnetic field?
This sounds like a science history question, but is not. It is about acceptable forms for the Lagrangian density of electromagnetism. There is also a second question on the distinction between total ...
- 91
3
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48
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Perturbation in Euler-Heisenberg Lagrangian
If we use minimal subtraction to remove infinities, the effective Lagrangian of the background EM field is:
$$ \mathcal{L}_{EH} = -\dfrac{1}{4}F^2_{\mu\nu} - \dfrac{e^2}{32\pi^2}\int \dfrac{ds}{s}e^{...
- 73