# 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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### A problem in an integration related to Wick rotation

In quantum field theory, we often calculate some integrations using Wick rotation. In the following, I will carefully deal with an integration involving Wick rotation. In the end, I have found that I ...
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### How to set up line integral of electric field? Confused over notation

In multivariable calculus the line integrals was parameterized and denoted: $$\int_C \mathbf{F} \bullet \, d\mathbf{r}=\int_D\mathbf{F}(\mathbf{r}(t)) \bullet \frac{d \mathbf{r}(t)}{dt} \, dt$$ ...
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### A function for calculating velocity at several distances as you fall towards the earth's center

Assuming there is no drag, no friction and no other objects affecting you. If you drop into the earth (through a tube). Your velocity will be 7900 m/s at the center of the earth according to http://...
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### Shifting integration variable and taking derivative seemingly giving problem

I am doing loop integral in quantum field theory, and an issue in shifting integration variable is giving me a problem. Let me illustrate with an example. I have an integral that looks approximately ...
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### Multidimensional Area and Volume

In 3D the volume is $xyz$, the product of three coordinates. But in $N$ dimension ,how to define area and volume?
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### Bridges between maths and physics: the $\tau=2\pi$ constant [closed]

[disclaimer: I am not a math or a CS major, this is probably an easy question for most people on Physics SE.] I just read the tau manifesto explaining - according to its author - the various ...
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### Difference between integral and differential physical laws [duplicate]

Why is integral and differential physical laws both used? I read that integral is global and differential is local. Could you tell me something about it?
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### Fourier transform in two dimensions, Green's function for Schrodinger equation

I want to calculate this Fourier transform: $$\int\limits_0^{\infty} \mbox{d}k \int\limits_0^{2\pi} \mbox{d}\varphi~ k \frac{e^{i \vec{k} \cdot(\vec{x}-\vec{x}')}}{k^2+B}$$ which will be 2D Green's ...
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### Interaction Potential for Damped Driven Pendulum

I'm trying to use the velocity Verlet integrator to simulate a damped driven pendulum (with unit mass) described by $\ddot{\phi}+\gamma \dot{\phi}+\omega_0^2 sin\phi=Acos(\Omega t)$ The Verlet ...
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### Energy stored in electric field [duplicate]

I know that energy stored in electric field / unit volume = $\frac{1}{2} \epsilon\,E^2$. so can I say that for any configuration calculating $\int \frac{1}{2} \epsilon\, E^2 \,d^3r$ over whole space -...
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### If the integral is zero when is the integrand zero? [closed]

Using Stoke's theorem we prove that the curl of the Electric field vanishes. This would be possible only if the integrand is zero when the integral is zero.
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### Why does work in the Work Energy Therom equal the Sum of the integral F*dr?

I am studying the work energy therom and I understand that 1/2(mv^2)=Wnet, however, I saw this picture below online. I understand the summation of the force times the change in distance. However, ...
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### How to integrate to find the view factor of two parallel disks of different radii? [closed]

You have two parallel coaxial disks of different radii. I have tables that give me the value as $$F_{ij} = \tfrac{1}{2} [S - \sqrt{S^2 - 4(r_j/r_i)^2}]$$ where $$S = 1 + \frac{1 + R_j^2}{R_i^2}$$ ...
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### Commutation relations in Quantum Field Theory [closed]

\begin{align} [a, a^\dagger] =& \left[\int d^3 x e^{-ikx} (\omega \phi(x) + i \Pi^\dagger(x)), \int d^3 x' e^{ikx'} (\omega \phi^\dagger(x') - i \Pi(x')) \right] \\ =& \int d^3x \, d^3x' \, e^{...
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### Slow-roll approximation for potential $V=\frac{1}{2}m^{2}\varphi^{2}$

I'm attempting to derive a solution to the slow-roll approximation for a scalar potential of the form $V=\frac{1}{2}m^{2}\varphi^{2}$. For the solution for $a(t)$ I will start by taking the slow-roll ...
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### Divergence theorem for cylindrical coordinates [closed]

I have a Vector field in a cylinder where x^2+y^2=4 and goes from z=0 to z=3 and a vector field A=(4x)i-(2y^2)j+(z^2)k and I'm trying to verify the divergence theorem for the vector field i set set ...
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### Electric field integration? [closed]

If we have a rod uniformly charged with $Q$ stretching from $-a$ to $a$ on the $x$-axis as shown in the picture And we want to calculate electric field in point $2a$ on the $x$-axis, we know that ...
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### Motivation for integrals over scalar field

I'm looking for good examples of physical motivation for integrals over scalar field. Here is an example I've seen: If you want to know the final temperature of an object that travels through a ...