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User twistor59 has addressed the part regarding the "generator" terminology, but let me give a bit more detail on the second part of the question. I'm going to restrict the discussion to matrix Lie groups for simplicity. Some background. Given a Lie group $G$ with Lie algebra $\mathfrak g$, there exist two mappings $\mathrm{Ad}$ and $\mathrm{ad}$, both ...

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If you have a basis for the Lie algebra, you can talk of these basis vectors as being "generators for the Lie group". This is true in the sense that, by using the exponential map on linear combinations of them, you generate (at least locally) a copy of the Lie group. So they're sort of "primitive infinitesimal elements" that you can use to build the local ...

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Consider a uniform rod of length $L$ pivoting and sliding on a horizontal plane. Kinematics You want to describe the relationship between the coordinates (and their derivatives) $x$ and $\theta$ and the motion of points A, B, and C. Position Kinematics $$\begin{matrix} \vec{r}_A = x\,\hat{i} & \hat{i} = (1,0,0)\\ \vec{r}_B = \vec{r}_A + ... 0 You haven't told where you have difficulties understanding such simple thing even after doing some research online. I think, Wikipedia has clear description of both. Historically, there were three branches of classical mechanics: Statics: The study of equilibrium and its relation to forces. Kinetics: The study of motion and its relation to forces. ... 0 Actually the story of the tensor product, which is typically told as an axiom in the world of quantum information, comes from the relativistic electron theory of Dirac. In relativistic quantum mechanics one wavefunction is replaced by 4 wavefunctions, and a suitable contraction leads to a two-element array (1,0) or (0,1) which we call the spin. In the case ... 1 I am not sure about this, but I think a “measure equation” is something astronomers seem to like a lot:$$ \frac\Gamma H \approx \left( \frac T{1.6\cdot 10^{10} \, \mathrm K} \right)^3 $$Or for absolute, relative magnitude and distance (although I am sure I mixed something up):$$ m - M = 5 - 5 \log\left(\frac{R}{10 \, \mathrm{pc}}\right)  So equations ...

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So, out of lack an already established name, I called it excitation states in: P. Migdał, J. Rodriguez-Laguna, M. Lewenstein, Entanglement classes of permutation-symmetric qudit states: symmetric operations suffice, arXiv:1305.1506.

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The speed of light is entirely a local concept - it does not care if there are 10 atoms or 10 billion galaxies somewhere in the Universe. Obviously we can't go to distant galaxies to directly measure the speed of light, so in the absolutely strictest sense this is not directly empirically tested. However, the constancy of the speed of light is one of the ...

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It is common to substitute $\gamma = 2 \zeta \omega_0$. The dimensionless constant $\zeta$ is referred to as the damping ratio. This damping ratio expresses the level of damping relative to critical damping.

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I would say no, the symplectic form isn't a physical quantity. It's rather a quantity specific to the phase space formulation of a physical system. If you choose not to formulate things in phase space, the symplectic form is absent. Moreover, even if you do work in phase space, in a system with constraints, the physical quantities are really only defined ...

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This is probably a question for Biology.SE however the tiny packets are just that, very small sacks of water. Think tiny drops. There is so little water that it doesn't take much energy to heat it up via infrared radiation and the cell can detect the temperature change.

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Adiabatic means quasi-static and isoentropic - slow enough to create negligible amount of irreversible excitation. This is the common rationale of technically different definitions. E.g., Landau & Lifshic'es definition has two components - thermally isolated (to prevent entropy change by heat exchange) and slow (to prevent irreversible excitation). For a ...

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The etymology of adiabatic appears to be from the Greek meaning "not passable" (native Greek speakers should feel free to clarify and/or correct that). In the technical meanings, the "passing" refers to heat transfer. So in thermodynamics, adiabatic means there is no heat transfer between the system and the environment. In practice, of course, that's an ...

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The terminological mismatch arises because different physicists use the terms differently in different contexts. For example, here is how Landau and Lifshitz define an adiabatic process in the context of thermodynamics: Let us suppose that a body is thermally isolated, and is subject to external conditions which vary sufficiently slowly. Such a process ...

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It is a matter of confusing terminology , at the present times when so much differentiation has happened in physics related scientific disciplines. Radiation was a general terminology assigned to transfer of energy radially, to start with with waves: acoustic waves, waves in water. Then came Maxwell's equations and the discovery of electromagnetic waves, ...

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