# 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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### On the convergence of an Euclidean path integral in 0+0D

Suppose we have an integral $$Z(\lambda) = \frac{1}{\sqrt{2\pi}}\int^{+\infty}_{-\infty} dx e^{-\frac{x^2}{2!}-\frac{\lambda}{4!}x^4}.$$ To my knowledge this is a possible integral which can arise in ...
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### Electrostatic potential of finite charged wire

So I was trying to find the electric potential at any point $\boldsymbol{x}$ of a charged wire of length $L$ at the $z$ axis, from $-L/2$ to $L/2$, and I had to write it down in terms of elliptic ...
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### Variation of Action and Border Terms

I need to compute the following very general (piece of) variation: \begin{equation} \int d^4x \delta (\sqrt{-g} R ) f \tag{1} \end{equation} where $R$ is Ricci scalar and $f$ a generic scalar ...
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### How to integrate out the Goldstone phase in effective Ginzburg–Landau (GL) action for BCS?

In page 293 of Altland and Simons' "Condensed Matter Field Theory", just above equation (6.38), in the process of deriving the London equations from the BCS path integral, the authors say, &...
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### Riemann-Lebesgue lemma in Faddeev-Kulish approach

I am learning about the established formalism used in the literature of IR divergences and dressed states, and I invariably come across an argument of the following form when evaluating a (photon) ...
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### Dot product of displacement vector with gradient [closed]

I have an integral like Eq. E.21 in Giamarchi's book (Appendix E, Quantum Physics in 1-D) : $I=\int d^2R \int d^2r (r\cdot\nabla_R \phi(R))^2 e^{-f(r)}$ where, $r=r_1-r_2, R=\dfrac{r_1+r_2}{2}.$ How ...
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### Maxwell Boltzmann speed distribution: why isn't speed element integrated when converting from velocity distribution? [duplicate]

Maxwell Boltzmann velocity distribution is given by $$f_{\vec v}(v_x,v_y,v_z)=A^{3/2}\exp{[B(v_{x}^{2}+v_{y}^{2}+v_{z}^{2})]}$$ To convert the velocity distribution into speed distribution, spherical ...
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### How to integrate "recursive" pressure/temperature relations?

I hope the term recursive is correct in this context. The Clausius-Clapeyron relation says that: $\frac{dP}{dT} = \frac{L}{T\Delta v}$ Where P is the pressure, L is the latent heat of vaporization, T ...
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### Modified Boltzmann statistics

I want to compute the following integral: $$p(E_i, \lambda) =\frac{L}{Z} \int_{-\infty}^{\infty}dt e^{it}\frac{1}{\lambda E_i +it}e^{-L\mathrm{tr}\log(\lambda H +it)}$$ in the limit of large $L$, ...
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### Fermionic measure in path integral

When writing the fermionic path integral one arrives at an expression containing $\mathcal{D}\bar{\psi}$ and $\mathcal{D}\psi$: $$\int \mathcal{D}\bar{\psi} \mathcal{D}\psi e^{iS}$$ Usual ...
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### An Integral from Feynman & Hibbs [closed]

In Appendix "Some Useful Definite Integrals" of Feynman & Hibbs "Quantum Mechanics and Path Integrals" they use some integral formulas(1) that I'm struggling to derive, and ...
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### How do I assign momenta for internal loops of a Feynman diagram?

I've been working on the one-loop corrections, and encountered the following diagrams: [a] and [b] come from the Yukawa Lagrangian $\phi\bar\psi\psi$. We can assign the momentum $k$ to one of the ...
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Work done is given by the integral $$\int \vec F\cdot d\vec r$$ Where $\vec F$ is force and $d\vec r$ is displacement. Writing displacement in terms of velocity, we get \int\vec F\cdot\vec v\,dt=\...