# 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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### Derivatives of distributions in general relativity

I am having some trouble when trying to reproduce some calculations involving the description of distributions (mostly used in spacetime junction conditions). I am trying to reproduce the ...
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### $D$-dimensional Schrodinger's equation with a Dirac delta potential

I know that for $D\geq 2$, there is no bound state for a Dirac potential $V=-\alpha \delta(\textbf{x})$ unless we use an ultraviolet cutoff $k_{max}=1/a$. I showed this by solving the Schrodinger's ...
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### Free path distribution

I'm studying statistical mechanics, and I'm trying to resolve some problem known from my thermodynamics course. So I want to calculate mean free path for particles with a concentration $n$ and ...
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### How can the propagator be written in the below integral form?

I’am finding it difficult to understand as to how the delta function is written as a product of many delta functions with the integral
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### Half of Dirac Delta within spectral integration

I was taking a course in Quantum Information along this last semester, and apart from some mathematical details it all made sense to me. One of these mathematical tricks that I haven't been able to ...
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### Classical field theory: marriage of differential geometry to functional analysis?

I have always wondered (and thoroughly - but perhaps not enough - searched for literature) how the purely geometrical formulation of classical field theory (take for example a hardcore text on this ...
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### Why is it physically resonable to consider a function as a regular distribution?

In "Mathematical Methods in Physics" by Blanchard and Brüning the introduction of regular distributions and then general distributions is motivated by the following idea: When we think about the ...
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### Under what circumstances is the functional derivative (of an action functional) an actual function?

In general, for a functional $F[\phi]$, the functional derivative is $$\frac{\delta F[\phi]}{\delta \phi} [f(x)] = \lim_{\varepsilon \to 0} \frac{F[\phi + \varepsilon f ] - F[\phi]}{\varepsilon}$$ ...
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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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### Are vacuum expectation values distributions?

In PCT, Spin, Statistics and all That (1964) on page 106 the vacuum expectation value is introduced in the following way. The question concerns the highlighted area, that is how can a tempered ...
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### Calculation of the Poisson bracket of a (Classical) Yang-Mills generator

This question might be too technical or minute, but I believe someone can give me the right advise. What I want to calculate is a Poisson bracket algebra of classical YM gauge generators, \begin{...
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### Finding the moments of the Boltzmann/Gibbs Distribution

I am trying to compute the moments of the Boltzmann distribution using a moment generating function, by taking the Fourier transform of the distribution and then taking derivatives to find the ...
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### Interpretation of induced force between two Dirac delta potential wells

This problem is based on MIT OCW course 8.04 problem set 6 question 5(e). https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/assignments/MIT8_04S13_ps6.pdf Consider two Dirac ...
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### Different definitions of Functional Derivative

In studying QFT and General Relativity, I came across two different definitions of Functional Derivative, and I'd like to know if they are equivalent. Firstly, in Wald's book General Relativity, as ...
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### Density of a thin disk by delta Dirac function

How to write a volume (charge for example) density using delta Dirac function in spherical coordinates in this case: There are thin charged disk (radius $a$) with surface charge density $\sigma$. The ...
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### Can Maxwell's Equations in differential form be viewed as equalities of measures?

What I have in mind is the following - Suppose we choose to model the universe as a 3 dimensional flat Euclidean space $\mathbb{R}^3$ equipped with the standard topology and the Borel-sigma algebra. ...
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### Counting experiment and standard error

I have a counting experiment: Let's say I have N identical bees. I take one of them, expose it to $\gamma$-radiation and look if it has died or survives. If it survives, I count it as 1 count. If it ...
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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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### What is dipolar charge distribution?

An electric dipole is a system of two opposite point charges when their separation goes to zero and their charge goes to infinity in a way that the product of the charge and the separation remains ...
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### What is the symmetry behind this degeneracy?

I was working on a quantum mechanics problem, involving the perturbation of the 3D cubical potential well: Suppose we perturb the infinite cubical well \begin{equation} V(x,y,z)=\begin{cases} 0, \...
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### Derivation of the QFT Propagator

I don't understand how we get from the RHS to the last line. \begin{eqnarray} \left[ \hat{H}_x - i \frac{\partial}{\partial t_x} \right] G^+(x,t_x,y,t_y) &=& -i \delta (t_x - t_y) \sum_n{\...
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### Bosonic Pair Distribution Function

In Schwabls Book "Advanced Quantum Mechanics" in the chapter for Bosons he calculates the Bosonic pair distribution function for noninteracting bosons. He said the expectation value of \begin{align*} \...
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### Dirac delta normalization of electromagnetic fields

Usually, to quantize electromagnetic fields we use box normalization and therefore the normalization constant contains the dimensions of Volume V of the box. But if we perform the Dirac-delta ...
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### A Naive Question about Delta Function and Wick Rotation

A delta function can be written as $$\delta(x)=\frac{1}{2\pi}\int_{-\infty}^{+\infty}dp\,e^{ipx}.$$ I have a very poor understanding of the Wick rotation technique used in quantum field theory. ...
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### Curl of magnetic field produced by current carrying wires with infinitesimal small area

Can Magnetic fields produced by thin current carrying wires with infinitesimal area have curl with a delta function in it ?? As area is Zero current density J definitely becomes infinite at where ...
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### How to plot the graph of this expression which involves Dirac delta function?

I was doing a problem on electrostatics which required finding the charge density from the given electric field and then plot a graph of the charge density. I was able to find the charge density which ...
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### Green's function regularization and delta distribution

I have a free Green's function which is proportional to a $2\times 2$ matrix: $$G_0 = \frac{1}{E^2-E_k^2}\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ The total Green's function after ...
The problem asks for a proof of the following equation, and I have no idea on how to approach this: $\int dx dp \delta(E-\frac{p^2}{2m}-\frac{m \omega^2 x^2}{2})f(E) = \frac{2\pi}{\omega}f(E)$ , for ...