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The justification of interpreting the energy band gradient with the velocity comes from semiclassics, and it turns out that the formula you give is correct only in certain circumstances and only to leading order. To attribute these terms to multiparticle effects is misleading, they are due to neglecting transitions to other bands, and they occur even if you ...

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It is all over the place, but it's involved. It is normally calculated from the path integral propagator. The most concise source of the radial Green's function you are after is eqn (15) of Grosche 1998, in terms of modified Bessel functions, integral rep,  G_l^C(r'',r';E) = \int_0^\infty\dfrac{e^{i e^2s''/\hbar}ds''}{\sqrt{v'v''}} ...

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The mathematical framework that I am familiar with for abelian p-form gauge theory (the one promoted by Freed, Moore and others) is that of Cheeger-Simons differential forms. In this framework, the space of topologically trivial p-form gauge fields over a manifold $X$ (the analogue of 1-form gauge fields on the trivial $U(1)$ bundle) are identified with the ...

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Too many words. Signal amplification is a fact. Negative power is an attempt to clarify a concept of stray reactances leading to a mathematical solution known as a "power factor" - not a fact. "P:ower" refers to the ability to perform work when force(pressure/voltage) is combined with the capacity to deliver "energy" (electrical current. or current of ...

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The question is given as a practice problem in Poisson's book "Relativists Toolkit" (p. 159, problem #7) along with some helpful hints. The tensor $\gamma_{ab}$ (which is not a tensor at all) must be defined in the following way: Let $h_{ab}$ be the induced 3-metric on the spacelike hypersurface $\Sigma$, and let on its boundary, $\partial \Sigma$, be ...

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