# Tag Info

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In relativity (both special and general) one of the key quantities is the proper length given by: $$ds^2 = g_{\alpha\beta}dx^\alpha dx^\beta \tag{1}$$ where $g_{\alpha\beta}$ is the metric tensor. The physical significance of this is that if we have a small displacement in spacetime $(dx^0, dx^1, dx^2, dx^3)$ then $ds$ is the total distance moved. You ...

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"Naturally" means in this case that the Kähler manifold appears out of the other ingredients of the theory without us putting in a Kähler structure by hand. "Natural" in such mathematical contexts often means that there is no choice for a certain structure, it just appears from the other parts of the theory. In this case, the Kähler geometry appears out of ...

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John has already given a nice intuitive answer, I'd like to write it in a bit more mathematical way. First of all metric means a bilinear defined over a product (vector) space: $g(v,w): V \times V \rightarrow \mathbb{R}$. Where the vectors $v,w$ lie in the vector space $V$. This bilinear should be smooth, symmetric $g(v,w) = g(w,v)$, and positive definite , ...

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Rotational and turbulent motion cannot "deepen" the gravity well in a galaxy of galaxy cluster. The contribution of kinetic energy to the stress-energy tensor is negligible compared to the rest-mass energy in non-relativistic systems. Assuming you mean something like, 'how does rotational and turbulent motion contribute to the equilibrium configuration of ...

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I asked myself the exact same question. This PDF file from Harvard says that indeed diffraction gratings should be instead called interference gratings (page 13, first paragraph of "Remarks"). EDIT : Here is the paragraph from the link, as suggested by @Kyle Kanos : A diffraction grating should more appropriately be called an “interference grating,” ...

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Is the Sun absorbing energy from it's surroundings? No, of course not in a net sense. The Sun loses far more energy than it absorbs from its surroundings. It is not in thermal equilibrium. The Sun is also not a blackbody at a single temperature, even though it most definitely absorbs nearly all radiation that is incident upon it. That is because the Sun is ...

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A pseudo Riemannian manifold is a manifold equiped with a metric of signature $(p,q)$, $p$ indicating the number of positive eigenvalues and $q$ the negative eigenvalues. For a Riemannian manifold, $q = 0$. A spacetime of dimension $n$ is defined by a pseudo-Riemannian manifold of signature $(1, n-1)$, or alternatively $(n-1,1)$, also called a Lorentzian ...

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A n-particle reducible diagram is a diagram that can be cut into two pieces if one cuts n or less lines. Conversely, a n-particle irreducible (n-PI) diagram cannot be cut into two pieces if one cuts n lines. The sunset diagram is 3-particle reducible, since it has 3 internal lines, but it is both 1-PI and 2-PI, and contributes to the self-energy (which ...

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