# Questions tagged [dirac-delta-distributions]

Distributions are generalized functions, such as, e.g., the Dirac delta function. DO NOT USE THIS TAG for statistical probability distributions, profiles, graphs, plots, etc.

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### How to do the integrals over the multivariate delta function?

How to do this integration? $$\int_{-\infty}^{\infty}dq\int_{-\infty}^{\infty} dp \; \delta(E-\frac{p^2}{2m}-\frac{k}{2}q^2)= 2\pi\sqrt{\frac{m}{k}}$$ I obtained the result using Mathematica, I am ...
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### Using Delta Dirac function as a mathematical tool in Green's functions

So, I was studying green's functions and in general I understood that if I have an operator $\mathscr{O}$ that acts of a function $h_1(\vec{r})$ such that $$\mathscr{O}h_1(\vec{r})=h_2(\vec{r})$$ ...
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### Towards a matrix element definition of PDF

In Schwartz's book, 'Quantum Field Theory and the Standard Model' P.$696$, he starts to derive an expression for a parton distribution function in terms of matrix elements evaluated on the lightcone. ...
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### Group theory, character, representations, delta function, unit element

I am reading a physics paper (hep-th/9204083 v1 above eq (4.15)) where there is a nice formula that reads $$\delta(U-\mathbb{1}) = \sum\limits_{r} \dim(r)\, \mathrm{tr}_r(U)$$ Here $\:U\:$ is a ...
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### Singularity of $B$-field in a Dirac String

I was assigned this question related to Dirac strings: Given a vector potential $\vec{A}= \frac{1-\cos(\theta)}{r\sin(\theta)}\hat{\phi}$, show that there is a singularity in the B field ...
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### Charge density as Dirac delta function

I little bit confused while I'm trying to convert a cylindrical charge distribution to spherical. The question is: A uniformly charged thin disk of radius $a$ and surface charge density $\sigma$ ...
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