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## New answers tagged hamiltonian-formalism

0

The most basic definition of a fluid is a fluid is a substance that continually deforms (flows) under an applied shear stress. To model a fluid using the Euler equations, you need to satisfy the condition that the mean free path of a particle, $\ell$, is significantly smaller than the typical size of the domain, $L$ (and also that viscosity and heat ...

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An approach alternative to that discussed by David Bar Moshe is to start from a different coordinate system in the Rindler wedge $W_R$: $$ds^2 = e^{2y}(−g^2dt^2+dy^2)$$ here $t, y \in \mathbb R$. The relation with the standard spatial coordinate in $W_R$ is $x=e^y$, where $x>0$ is related with the alternate form of the (same) metric: $$ds^2 = -g^2 x^2 ... 2 The dynamics of a classical point particle moving in the background of any curved space-time is always Hamiltonian (with respect to the canonical symplectic form), thus automatically satisfying the Liouville’s theorem. This is because the action functional is given by the integral of the line element:$$ I = -m \int ds = -m \int \frac{ds}{dt}(q, v) dt = ...

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You can only find the Hamiltonian if you do a so-called 'gauge fixing' procedure, since the Dirac field couples (minimally, but uniquely) to a gauge field. To get the Hamiltonian (density) you need to perform the full Dirac constraint analysis and at the end 'gauge fix'. See the books by Sundermayer or Henneaux+Teitelboim for details regarding the ...

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