# Search results

1. ### A Off-Forward quark-quark amplitude in momentum space

I am having difficulty writing out ##\bra{p',\lambda}\psi^{\dagger}(-\frac{z^-}{2})\gamma^0\gamma^+\psi\frac{z^-}{2})\ket{p,\lambda}## in momentum space. Here, I am working in light-cone coordinates, where I am defining ##z^-=z^0-z^3##, ##r'=r=(0,z^{-},z^1,z^2)##. My attempt at this would be...
2. ### Special Relativity Muon problem

By the logic of my argument, I simply mean that is showing the time of of travel less than the time of decay sufficient to show that the muon would have to reach the ground. I have recently contacted my professor however, and they said this form of argument dosen't work, and I would have to give...

9. ### A Propagator is Phi^4 Theory

In this case, the lagrangian density would be $$\mathcal{L}=\frac{1}{2}((\partial_{\mu}\Phi)^2-m^2\Phi^2)-\frac{\lambda}{4!}\Phi^4$$ whe $$\Phi$$ is the scalar field in the Heisenburg picture and $$\ket{\Omega}$$ is the interacting ground state. Was just curious if there were ways to do Feynman...
10. ### Phi 4 Theory Propagator Question

I know in the Heisenburg picture, $$\Phi(\vec{x},t)=U^{\dagger}(t,t_0)\Phi_{0}(\vec{x},t)U(t,t_0)$$ where $$\Phi_{0}$$ is the free field solution, and $$U(t,t_0)=T(e^{i\int d^4x \mathcal{L_{int}}})$$. Is there a way I could solve this using contractions or Feynman diagrams? Because otherwise, it...

13. ### A Scattering Amplitudes for Phi 4 Theory

Never mind. Figured it out. I would have to go to $$\lambda^2$$ in the expansion. Thanks.
14. ### A Scattering Amplitudes for Phi 4 Theory

I know $$i\mathcal{M}(\vec {k_1}\vec{k_2}\rightarrow \vec{p_1}\vec{p_2})(2\pi)^4\delta^{(4)}(p_1 +p_2-k_1-k_2)$$ =sum of all (all connected and amputated Feynman diagrams), but what is meant by 1 loop order? In other words, when I take the scattering matix element...
15. ### I Ground State in Peskin and Schroeder

Nevermind, I think I figured it our. I mistakenly assumed the $$e^{-iE_n T}\to 0$$ as $$T\to \infty$$, but that is not the case, which is why the substitution is needed.
16. ### I Ground State in Peskin and Schroeder

In P&S, it is shown that $$e^{-iHT}\ket{0}=e^{-iH_{0}T}\ket{\Omega}\bra{\Omega}\ket{0}+\sum_{n\neq 0}e^{-iE_nT}\ket{n}\bra{n}\ket{0}$$. It is then claimed that by letting $$T\to (\infty(1-i\epsilon))$$ that the other terms die off much quicker than $$e^{-iE_0T}$$, but my question is why is this...
17. ### I Energy-Momentum Tensor Question

Apologies, that should be $$\Pi^{\mu}\partial^{v}\phi$$ where $$\phi$$ is a field and $$\Pi^{\mu}=\frac{\partial \mathcal{L}}{\partial(\partial_{\mu}\phi)}$$. Originally had this posted to the High Energy subforum since this was originally a quantum field theory question, but someone moved it here.
18. ### I Energy-Momentum Tensor Question

I know the tensor can be written as $$T^{\mu v}=\Pi^{\mu}\partial^v-g^{\mu v}\mathcal{L}$$ where $$g^{\mu v}$$ is the metric and $$\mathcal{L}$$ is the Lagrangian density, but how would I write $$T_{\mu v}$$? Would it simply be $$T_{\mu v}=g_{\mu \rho}g_{v p}T^{\rho p}$$? And if so, is there a...

21. ### Phi 4 Theory Renormalization

Let ##\phi_{+}=\frac{d^3k}{2\omega_k (2\pi)^3}\int(\hat{a}^{\dagger}(\overrightarrow{k})e^{ikx})## and ##\phi_{-}=\frac{d^3k}{2\omega_k (2\pi)^3}\int(\hat{a}(\overrightarrow{k})e^{-ikx})##. Then ##\phi^4=\phi_{1}\phi_{2}\phi_{3}\phi_{4}=(\phi_{1+}+\phi_{1-})(\phi_{2+}+\phi_{2-}...
22. ### A Exploring Solutions to $\phi$ and $\ket{\overrightarrow{P}}$

I already know this quantity diverges, however I was wondering where to go from there. Any resource would be appreciated. Thank you. Useful Information: $$\phi=\int\frac{d^3k}{2\omega_k (2\pi)^3}(\hat{a}(\overrightarrow{k})e^{-ikx}+\hat{a}(\overrightarrow{k})^{\dagger}e^{ikx}))$$...
23. ### Trouble Writing Equations

Thank you, this works. The math script just wasn't working when I tried previewing it in the homework forums, but worked when I actually posted it.
24. ### \Phi^4 Integral

From this, I find $$\bra{P'} \phi^4 \ket{P} = \int \frac {d^3 k_1 d^3 k_2 d^3 k_3 d^3 k_4} {16 \omega_{k_1}\omega_{k_2}\omega_{k_3}\omega_{k_4} (2\pi)^{12} }\bra{0} a_{P'}(a_{k_1} a_{k_2} a_{k_3}a_{k_4}e^{i(k_1+k_2+k_3+k_4)x}+...)a^{\dagger}_{P}\ket{0}$$ (a total of 16 different terms) Right...

38. ### Scattering Cross Section

I considered that, but I don't think that method would quite work since l is a summation to infinity.
39. ### Scattering Cross Section

So, I talked with my professor, and apparently, there was a typo. It should be that $$\frac{d\sigma}{d\Omega}=\alpha+\beta cos(\theta)+\gamma cos^2(\theta)$$.

44. ### A Gauge Invariance of the Schrodinger Equation

Perhaps it is a silly question. I was just wondering why it held. Thank you.

48. ### Heat Capacity of a Fermi Gas at Low Temperature

Thank you. Just one more question. Would the limits of integration just be from 0 to $$\infty$$?