All Questions
Tagged with homework-and-exercisesintegration
345 questions
0votes
0answers
45views
How can I write the solution of this center of gravity problem, without having to write what method I have in mind or the method that I am using? [closed]
Long ago in a handout on Mechanics, I remembered it had a part focussing on how to calculate the center of gravity from a remaining portion of a body, i.e. the center of gravity of the body when a ...
2votes
1answer
65views
Computing position two-point function and Fourier transform of $p^4 \ln p$
I am computing a two-point correlator in 4D Euclidean space and I am struggling with one particular term. I have found that in momentum space my correlator goes as $$\langle \mathcal{O}(p)\mathcal{O}(...
10votes
4answers
903views
Asymptotic integral in Peskin & Schroeder, Problem 6.3
The question is about P&S QFT Problem 6.3. In question (a), the contribution to $a = \frac{g - 2}{2}$ from Higgs boson is calculated, the result is: $$ \delta a = \frac{\lambda^2}{16 \pi^2} \int_0^...
- 453
3votes
1answer
141views
Integration in Fujikawa method
It is from anomalies in quantum field theory by Reinhold A. Bertlmann First is trivial. I can solve the second integral using $\xi =k^{\mu}k_{\mu}$, $$ \int d^{4}k e^{-k^{\mu}k_{\mu}} k_{\mu}k_{\nu} = ...
- 83
1vote
0answers
97views
A 1d Feynman integral: How to compute?
I am trying to evaluate the following integral: $$ I_{n_1,n_2,\alpha} \,=\, \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \, \bigg(\,{ \frac{e^{...
- 604
0votes
1answer
48views
I would like to understand an algebra step in the derivation of the decay rate of the classical model of an electron orbiting an atom
In the solutions guide to a problem set I see the following two equations, but I do not understand why the bounds of integration on the left become $r_i$ to $r_f$ since we are integrating with respect ...
4votes
1answer
100views
Comparision of time taken between two points along different paths [closed]
I was wondering about a question which is as follows we have a body if mass $m$ at point (1,1) on the cartesian plane and gravity is acting along $-y$ axis. If we release the ball and there are $n$ ...
1vote
1answer
181views
Derivation of Rutherford scattering formula in Landau & Lifshitz mechanics book
This is from Landau & Lifshitz Mechanics book, p.49, the scattering formula (18.4) for general elastic scattering that gives the scattering angle On p.53 this formula is given, where just the ...
- 149
1vote
0answers
83views
Center of mass of a solid sphere with spherical cavity [closed]
As shown in figure, when a spherical cavity (centred at O) of radius 1 is cut out of a uniform sphere of radius R (centred at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, ...
-2votes
1answer
76views
I have been trying to solve this Gaussian integral, which comes up during the perturbation theory [closed]
This integral which comes up during finding first order correct in energy of a harmonic oscillator,where e^-(x-y)^2 is perturbation term $$\int_{-\infty}^{+\infty} \exp(-(x^2+y^2)-(x-y)^2) \ dx \ dy$$ ...
0votes
1answer
48views
Integrating acceleration + escape velocity over distance [closed]
I am not sure how to title this question so apologies if it's inaccurate. If I throw an object at thrice the escape velocity of earth, what would be its velocity very far away from earth, (at a ...
- 128
-1votes
1answer
117views
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: $$\int_m^{\infty}{\rho e^{-\rho r}\over\sqrt{\...
- 4,722
0votes
1answer
131views
Exponential decay of propagator outside lightcone
In Tong's lecture notes (http://www.damtp.cam.ac.uk/user/tong/qft.html) page 38, he calculates the following propagator: $$D(x-y) = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_\vec{p}} e^{-ip \cdot (x-y)}....
- 879
6votes
0answers
127views
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 ...
- 998
0votes
0answers
67views
Solution for the scale factor for a curved universe containing only matter
In my textbook, Introduction to cosmology by Barbara Ryden, the author gives directly the solution for the following integral if $\Omega_0 > 1$: $$H_ot = \int^a_0 \frac{da}{[\Omega_0/a + (1-\...
