All Questions
Tagged with quantum-field-theory homework-and-exercises
672
questions
1
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0
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49
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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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99
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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 ...
- 980
2
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2
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148
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Derivation of propagator for Proca action in QFT book by A.Zee
Without considering gauge invariance, A.Zee derives Green function of electromagnetic field in his famous book, Quantum Field Theory in Nutshell. In chapter I.5, the Proca action would be,
$$S(A) = \...
- 529
1
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0
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59
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Peskin and Schroeder page 201, solving integral over angular part
They make the following steps:
$$\int\frac{\Omega_\bf{k}}{4\pi}\ \frac{1}{(\hat{k}\cdot p')(\hat{k}\cdot p)} = \int_0^1d\xi\int\frac{\Omega_\bf{k}}{4\pi}\frac{1}{(\xi\ \hat{k}\cdot p'+(1-\xi)\ \hat{k}\...
- 327
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63
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Questions about computing the commutator of the Lorentz generator
I am computing the commutator of the Lorentz generators, from the Eqn (3.16) to Eqn (3.17) in Peskin & Schroeder.
$$
\begin{aligned}
J^{\mu\nu} &= i(x^\mu \partial^\nu - x^\nu \partial^\mu ) &...
- 41
1
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1
answer
73
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Peskin and Schröeder page 195, IR divergence in the electron vertex function, rewriting integral
Peskin and Schröeder make the following statement
$$\int_0^1dxdydz\ \delta(x+y+z-1)\frac{1-4z+z^2}{\Delta(q^2=0)}=\int_0^1dz\int_0^{1-z}dy\frac{-2+(1-z)(3-z)}{m^2(1-z)^2},\tag{p.195}$$
where $$\Delta =...
- 327
2
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2
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132
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Commutator of conjugate momentum and field for complex field QFT
In Peskin & Schroeder's Introduction to QFT problem 2.2a), we are asked to find the equations of motion of the complex scalar field starting from the Lagrangian density. I want to show that:
$$i\...
- 538
3
votes
1
answer
121
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Explict Form of Ground State in Interacting Field Theory
In An Introduction to Quantum Field Theory by Peskin and Schroeder chapter 4, it has discussed about the ground state $|\Omega\rangle$ (where $|0\rangle$ is the ground state in free field theory) in ...
- 529
1
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1
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71
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Trouble Understanding Computation In Nucleon Scattering Example in David Tong Lecture Notes
I am struggling to understand the following computation from page 59 of Tong's QFT notes
http://www.damtp.cam.ac.uk/user/tong/qft.html
The expression
$$
(-ig)^{2} \int \frac{d^{4}k}{(2\pi)^{4}} \frac{...
- 23
-1
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1
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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\...
- 7
1
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0
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60
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Feynman parameters for $n=3$
I proved the general formula for the Feynman parameters:
\begin{equation}
\frac{1}{P_1^{a_1}...P_n^{a_n}}=\frac{\Gamma(a_1+...+a_n)}{\Gamma(a_1)...\Gamma(a_n)}\int_0^1dx_1...dx_n\delta(1-x_1-...-x_n)\...
- 357
2
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1
answer
146
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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 ...
- 1,713
0
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0
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63
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Action of Conjugate momentum $\hat{\pi}$ on $\hat{\phi}$ eigenstate [duplicate]
So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum Field Theory and the Standard Model"
and in the second requirement, he wanted me to show that the action of the conjugate ...
0
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1
answer
208
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Time reversal operator and Dirac gamma matrices
How would you prove that $T^{-1}\gamma_\mu T=\gamma_\mu$? Being $T$ the time reversal operator defined as $T=\gamma_1\gamma_3 K$ with $K$ the complex conjugate operator and $\gamma$ the Dirac gamma ...
- 941
3
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1
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117
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Show that $i/2m\int d^3\vec x\hat\pi(\vec x)\partial^2_i\hat\phi(\vec x)=1/(2\pi)^3\int d^3\vec p E(\vec p)\hat a(\vec p)^\dagger\hat a(\vec p)$ [closed]
Show that the quantum field for the Hamiltonian, $$\hat H=\frac{i}{2m}\int d^3 \vec x\hat{\pi}(\vec x)\partial^2_i\hat{\phi}(\vec x)\tag{1}$$
can be written as $$\int \frac{d^3\vec p}{(2\pi)^3}E(\vec ...
- 295