# Questions tagged [integration]

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

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### How to get distance when acceleration is not constant?

I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question. The equation for distance of an accelerating object with constant ...
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### When is Lebesgue integration useful over Riemann integration in physics?

Riemann integration is fine for physics in general because the functions dealt with tend to be differentiable and well behaved. Despite this, it's possible that Lebesque integration can be more ...
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### Transformation of $d^4x$ under translation disregarded?

Under a translation in spacetime i.e., $$x\mapsto x^\prime=x+a,\tag{a}$$ a scalar field $\phi(x)$ $$\phi(x)\mapsto\phi^\prime(x)=\phi(x-a).\tag{b}$$ My aim is to verify the invariance of an action of ...
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### Gaussian integral with imaginary coefficients and Wick rotation

Although this question is going to seem completely trivial to anyone with any exposure to path integrals, I'm looking to answer this precisely and haven't been able to find any materials after looking ...
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### Recovering QM from QFT

Reading through David Tong lecture notes on QFT. On pages 43-44, he recovers QM from QFT. See below link: QFT notes by Tong First the momentum and position operators are defined in terms of "...
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### Why is the $dx$ right next to the integral sign in QFT literature?

I've noticed that in QFT literature, integrals are usually written as $\int \!dx ~f(x)$ instead of $\int f(x) dx$. Why?
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### Newton's original proof of gravitation for non-point-mass objects

Suppose we have two bodies, one very large (Earth), and one very small (a cannon ball). If the cannon ball is some distance away from the Earth, to find out the force produced on the cannot ball, we ...
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### How is the Saddle point approximation used in physics?

I am trying to understand the saddle point approximation and apply it to a problem I have but the treatments I have seen online are all very mathematical and are not giving me a good qualitative ...
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### Switching from sum to integral

I'm specifically asking about an equation in An Introduction to Quantum Field Theory, by Peskin and Schroeder. Example from page 374: $$\mathrm{Tr} \log (\partial^2+m^2) = \sum_k \log(-k^2+m^2)$$ ...
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### What it means to integrate over $n$ variables out of $N$, where $N>n$?

I was reading Theory of Simple Liquids, when I came across BBGKY hierarchy. In deriving the expression for the hierarchy, they integrate an integration of N variables over N-n variables to make the ...
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### Gaussian integral of a function with nonzero mean (generalizing Wick theorem)

From the wikipedia article, for a Gaussian integral of an analytic function we have that This is equivalent to the Wick theorem when f(x) is a polynomial. Now I'm trying to obtain a similar formula ...
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### The computation of the propagator in two dimensions

I did the computation of the propagator in two dimensions at (19.26) in Peskin & Shroeder as follows. First I performed a Wick rotation. \begin{alignat}{2} \int\frac{d^2 k}{(2\pi)^2}e^{-ik\cdot (...
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I am following the derivation of the field equations on the the Wikipedia page for $f(R)$ gravity. But I do not understand the following step: $$\delta S = \int \frac{1}{2\kappa} \sqrt{-g} \left(\... 3answers 189 views ### Why doesn't \vec{E} =\frac{1}{4\pi\epsilon_0} \int\frac{\rho \hat{r}\;dxdydz}{r^2} blow up at r=0, when \rho is finite? Electric field at (x,y,z) produced by a continuous distribution of charges is given by:$$\mathbf{E}(x,y,z) =\dfrac{1}{4\pi\epsilon_0} \int\dfrac{\rho(x',y',z') \mathbf{\hat{r}} \;\mathrm{d}x'\mathrm{...
In quantum field theory we always deal with complex integrals. They arise, e.g. when we calculate Feynman diagrams in either $T=0$, $T \neq 0$ and non-equilibrium formalism (or just Fourier transforms ...
Do the source terms multiplying a complex field and its conjugate need to be conjugates for the Gaussian identity to hold? E.g. is \int D({\phi,\psi,b}) e^{-b^\dagger A b +f(\phi, \phi^\dagger,\...