All Questions
Tagged with quantum-field-theory homework-and-exercises
670
questions
-1
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1
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Deriving the equal time anti-commutator of the Dirac fields [closed]
I am trying to solve an exercise on deriving the equal-time anti-commutator of the Dirac fields. But I got stuck somewhere and couldn't get the desired result.
I would like to show that
$$
\{\psi(x), \...
- 41
1
vote
1
answer
74
views
Asymptotic Freedom QCD
I'm trying to understand the derivation of asymptotic freedom with the renormalisation group equations. I'm reading Taizo Muta's book on QCD. What I don't understand is how he obtains the last ...
- 15
0
votes
0
answers
60
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How can I calculate the cross-section of a $N+\pi \rightarrow N + \pi$?
In the same theme as my previous question, I have the diffusion process $$N+\pi \rightarrow N + \pi$$ where the Lagrangian for this theory is
$$L = \partial^\mu\psi\partial_\mu\psi^* - M²\psi\psi^*-\...
- 11
0
votes
0
answers
31
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Embedding of spin-3 particle in a tensor $\phi_{\mu\nu\sigma}$
How can I show that a spin-3 particle can be embedded in a tensor $\phi_{\mu\nu\sigma}$ symmmetric under the exchange of any pair of indices?
- 7
1
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0
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38
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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:
$$
\mathcal{L}=\bar{\psi}_{L}i \gamma_{\mu}D^{\mu}...
- 81
0
votes
1
answer
87
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The Klein-Gordon Propagator According to Peskin and Schroeder (Derivation of *Retarded* Green's Function)
On page 29 of Peskin and Schroeder's An Introduction to Quantum Field Theory, the authors write that the propagator is given by:
$$\begin{align}
\langle 0|[\phi(x),\phi(y)]|0\rangle&=\int{d^3p\...
- 4,399
-1
votes
1
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64
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On causality for space-like intervals and the Klein-Gordon field: integral pg 27 of Peskin and Schroeder's Introduction to Quantum Field Theory [closed]
Note: this is not a duplicate: I am not interested in the issue of the contour, but in methods of integration.
I am desirous to integrate the following:
$$\int_m^{\infty}{\rho e^{-\rho r}\over\sqrt{\...
- 4,399
0
votes
1
answer
116
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Fourier transform of the Gaussian action for the real scalar bosonic field
In my current homework, we have to get familiar with quadratic theory in order to reach $\phi^4$-theory. So the starting point is
$$Z = \int Dx e^{-S[\phi]}$$
with the action for the real scalar ...
- 1
0
votes
0
answers
23
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Possible decays of a scalar particle, Feynman diagrams and calculation of branching ratio - Explenation of solution required
Consider the Lagrangian describing two Dirac fields of masses $m_1$ and $m_2$ and a scalar neutral field of mass $M$, which in addition to the free terms contains the following interaction term
\begin{...
- 17
1
vote
0
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67
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Derivation of massive photon propagator
I'm trying to derive the massive photon propagator using the path integral formalism for a theory with
$$
\mathcal{L} = -\dfrac{1}{4} F_{\mu\nu} F^{\mu\nu} + \dfrac{1}{2} m^2 A_\mu A^\nu, \text{with } ...
- 1,452
3
votes
1
answer
91
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How can I count diagrams (in this scalar QED example) at a particular order without drawing all the Feynman diagrams?
Here's a 3-loop diagram for light-by-light scattering in scalar QED (from Schwartz textbook question 9.2):
The question 9.2 asks approximately how many other diagrams contribute at the same order in ...
- 1,783
2
votes
1
answer
145
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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 ...
- 90
0
votes
1
answer
94
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Exponential decay of propagator outside lightcone
In Tong's lecture notes (http://www.damtp.cam.ac.uk/user/tong/qft.html) page 38, he calculates the following propagator:
$$D(x-y) = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_\vec{p}} e^{-ip \cdot (x-y)}....
- 665
1
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0
answers
48
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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 ...
- 35
6
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0
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98
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Fourier transform of Feynman Integral
In Nastase, Introduction to AdS/CFT, the first chapter talks a little about the star-triangle duality. In fact, it was claimed that the Fourier Transform of a Feynman-like diagram in position space in ...
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