Cylindrical Polar coordinates, Spherical Polar coordinates. which gives the gradient of a function f in spherical coordinates - refer back to. We are working in the rest frame of a meson with mass M M and the. Distribution Dirac delta function from Wikipedia Dirac delta. The delta function was famously introduced in physics by Dirac. Im working through a QFT problem and at one stage in the solutions we have this step: (4)(p q1 q2) (E1 +E2 M)(3)(q1 q2). In the end it is just an artificial problem that comes from an incorrect choice of coordinates. Factorising a 4D Dirac delta function in a rest frame. Or you simply use symmetry to make $\vec a$ not point in the $z$-direction. For this you can just choose different spherical coordinates with respect to some other axis than $z$. You have to make sure that your cover $\vec a$ with your domain. On the order hand, the delta function of a vector can be decomposed into the product of several delta functions, of the vector's components,į(\vec a)=\int f(\vec x)\prod_i\delta^3(x_i-a_i)\mathrm d x_i,\tag(\vec x - \vec a)), Where $f(\vec x)$ is an arbitrary function on the space, and $|J(\vec x)|$ is the Jacobian determinant. The delta-function is an example of what mathematicians call a generalized function : it is not well-defined at, but its integral is nevertheless well-defined. It satisfiesį(\vec a)=\int \delta^3(\vec x-\vec a)f(\vec x)|J(\vec x)|\mathrm d^3\vec x, The one-dimensional spike function is called the Dirac delta-function after the Cambridge physicist Paul Dirac who invented it in 1927 while investigating quantum mechanics. Let $\delta^3(\vec x-\vec a)$ represent a point density at $\vec a$.
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