All Questions
Tagged with renormalization homework-and-exercises
54
questions
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Asymptotic Freedom QCD
I'm trying to understand the derivation of asymptotic freedom with the renormalisation group equations. I'm reading Taizo Muta's book on QCD. What I don't understand is how he obtains the last ...
1
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39
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Loop Calculations of A Spontaneous Broken gauge theory with fermions
Let me first rephrase the background. Consider adding a massless fermion to the spontaneously broken $U(1)$ gauge theory through a chiral interaction:
$$
\mathcal{L}=\bar{\psi}_{L}i \gamma_{\mu}D^{\mu}...
2
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1
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147
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Derivative interactions in the Wilsonian renormalisation Group
I am currently working through some basic renormalisation group problems, and have come to one about derivative interactions. It has been a while since I have studied QFT formally so bear with me ...
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Problem solving for Wilsonian Effective Action
I'm currently doing some basic questions on renormalisation group, but I've ran into a wall when it comes to one particular step in an answer. The question is as follows:
This problem is a toy model ...
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130
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Massless Sunset Diagram $\phi^4$ [closed]
I should compute an explicit calculation for the sunset diagram in massless $\phi^4$ theory.
The integral is $$-\lambda^2 \frac{1}{6} (\mu)^{2(4-d)}\int \frac{d^dk_1}{(2\pi)^d} \int \frac{d^dk_2}{(2\...
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How to explain the reason of harmonic approximation by Wilson RG?
It's a part of my homework.
In many body physics, considering the hamiltonian of the ions, we often use harmonic approximation then the hamiltonian turns to
$$
H=\sum_{k}\hbar\omega(b^\dagger b+\...
2
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1
answer
147
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2-loop correction to exact 3-point vertex in a complex scalar field theory with cubed interaction
I am a graduate student with 1 quarter of relativistic QFT at the level of Srednicki (covered up to Chapter 30 this Fall). This question is not in any book that I know off and it wasn't assigned as ...
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External leg correction to 3-point QED Green's function
I am trying to calculate the following diagram to solve the Callan-Symanzik equation for the three-point Green's function (two massless fermions and a photon).
The counterterm to the photon ...
1
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1
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115
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Calculation of $ \gamma(\lambda) $ in massless renormalizable scalar field theory
In Peskin & Schroeder p.413 and 414, the Callan-Symanzik equation for a 2-point Green's function is used to calculate $ \gamma(\lambda) $ for a massless renormalizable scalar field theory. The two-...
0
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158
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Analyzing the one-loop self-energy graph in $\phi^3$ model
Consider the $\phi^3$ model with a real scalar field $\phi(x)$ in $3+1$ dimensional Minkowski spacetime with metric $(-,+,+,+)$. Its Lagrangian density is
$$
\mathcal{L}=-\frac{1}{2} \partial_\mu \phi ...
0
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54
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Beta function of CFT perturbed by several operators
As the title says, I am trying to derive the $\beta$ function of a CFT whose action is perturbed by several operators. The main refference I am following is https://arxiv.org/abs/1507.01960 starting ...
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102
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Beta function from renormalized coupling
While trying to derive a specific beta function for a CFT a stumbled upon the following. I have some bare coupling $g_b$ and introduce a renormalized coupling $g$ as
$$g_b=\mu^\epsilon(g+\frac{zg^2}{\...
3
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50
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Divergent verticies in mesonic scalar theory [closed]
Considering the following Lagrangian density:
$$ \mathcal{L} = - \frac{1}{2} ( \partial_{\mu} \phi \partial^{\mu} \phi + m^2 \phi^2) + \bar{\psi} (i \gamma^{\mu} \partial_{\mu} - m) \psi + g \bar{\psi}...
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414
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Yukawa decay at one-loop
I am trying to calculate the amplitude for a decay $\phi \to e^+e^-$ under a Yukawa interaction $\mathcal{L}_I = -g\phi \bar{\psi}\psi$ to one-loop order (with massless fermions for simplicity).
If I'...
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0
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From which interaction term does the self-energy diagram of $\phi^4$ theory come?
In 4D, let us start with the normal-ordered product of free neutral scalar fields $:\phi^4:$.
Then, we can in fact write $$:\phi^4:=\sum_{i=0}^4 V_i$$ where each $V_i$ is an operator-valued ...