# Tagged Questions

For questions about problems related to physics that involve evaluating integrals. Purely mathematical questions should be asked at math.SE.

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### Propagator in massless scalar field theory

Suppose we have the following Lagrangian: $\mathcal{L} = \frac{1}{2} \phi \Box \phi + V(\phi)$, where $\Box = \partial _ {\mu} \partial ^ {\mu}$ and $V$ is the interaction term. We use the $(-+++)$ ...
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### Coordinate Systems in Loop Integrals

Let us consider a two-point two-loop integral $\int \mathrm{d} ^ 4 k _ {2} \int \mathrm{d} ^ 4 k _ {1} \, f(k _ {1}, k _ {2}, p)$, where $k _ {1}$, $k _ {2}$ and $p$ are four-dimensional vectors in ...
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### Fraunhofer diffraction at circular aperture - integration of bessel function

I'm trying to understand the calculation here: http://en.wikipedia.org/wiki/Fraunhofer_diffraction_(mathematics)#Circular_aperture for the solution by integration, but I plain and simple fail to see ...
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### Shifting the integration variable in loop integrals

We know that, in four dimensions, shifting the integration variables is valid only for convergent and logarithmically divergent integrals. If we employ a hard cutoff $\Lambda$, is it permissible to ...
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### Equivalence of integrals in Classical Electrodynamics

I have a technical question about a section from Jackson's Classical Electrodynamics 3rd ed. In chapter 14, Jackson derives an expression for $\frac{d^2I}{d\omega d\Omega}$, the frequency spectrum ...
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### How to intergate the cross section over the surface of a detector?

My beam moves along the $X$ axis. I know the cross section $\frac{d \sigma}{d \Omega}$. My rectangular detector is perpendicular to the $XY$ plane and its surface is perpendicular to the line ...
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### Calculate the parabollic trajectory

In order to calculate the parabollic trajectory (or ballistic) I need intrinsic equation. Now I need to integrate this equation but I don't know how. I would appreciate so much if you help me!
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### Off-axial Field of Finite Solenoid

Regarding the computation of the off-axial field of a finite solenoid: The Radial and Z components of the off-axial magnetic field of a solenoid are given as: \begin{align} B_r &= \frac{\mu ni}{\...
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### Integrating Charged Bodies

Why is it possible to integrate charged bodies by first taking a small charge and adding more small charges around it? Wouldn't the similarly charged particles exert an immense amount of force on ...
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### Fourier Transforming a $n$-dimensional ket (QM)

I would like to evaluate the Fourier Transform of $n$ functions. I am aware from the derivation of the convolution how this is done for the case of $n=2$. How could this be generalised for $n=3$? ...
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### How can one approximate integral def. of Z by the max value of the integrand?

I am taking a course in statistical physics, and while reviewing my notes from the lectures I came across something that I cannot get my head around. We arrive at an integral expression for the ...
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### Verlet timestep

I am using velocity Verlet in molecular dynamics. Is just a simple question, if a simulation using time-step femtosecond, in velocity Verlet is just necessary $dt = 10^{-15}$ to use femtosecond?
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### Geometric Interpretation of these equations of motion?

I was reading my Engineering Mechanics book, and it derived some strange looking integrals I'll have to apply. I could memorize them, but I'd rather understand them - then I won't have to memorize. ...