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network profile
| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 1 year, 5 months |
| seen | 7 hours ago | |
| stats | profile views | 251 |
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Jul 24 |
answered | What does symplecticity imply? |
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Jul 22 |
awarded | Citizen Patrol |
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Jul 22 |
answered | Units of Distance, Pressure, and Temperature |
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Jul 21 |
comment |
Hamiltonian mechanics and special relativity? +1: thanks a lot for that link; my own musing went into the direction of modeling relativistic mechanics via local contact structures on the space of geodesics parametrized by arc length (ie proper time); that's just another way to arrive at $J^1_1Q$, and now that I know where I need to end up eventually, I might revisit that idea... |
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Jul 20 |
comment |
QM without complex numbers @kηives: the space of states for a finite-dimensional quantum system is the complex projective space $P_n\mathbb{C}\cong\mathbb{C}^{n+1}\setminus\{0\}/\mathbb{C}^*\cong U(n+1)/U(n)\times U(1)\cong S^{2n+1}/S^1$ |
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Jul 20 |
answered | QM without complex numbers |
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Jul 19 |
comment |
Introduction to differential forms in thermodynamics @Ron: I don't believe that article is paywalled (I just accessed the PDF from home and via a free proxy); in section 8, it is shown that the equations of state of the ideal gas fix a lagragian submanifold of a symplectic space as an example of the interpretation of the legendre transformation in context of symplectic geometry |
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Jul 19 |
comment |
What's the meaning of the general solution and the particular solution in differential equations? @Ron: I slightly reworded the last part |
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Jul 19 |
revised |
What's the meaning of the general solution and the particular solution in differential equations? added 30 characters in body |
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Jul 19 |
comment |
Introduction to differential forms in thermodynamics @Ron: re Legendre transformation, I was thinking along the lines of section 8 of numdam.org/item?id=AIHPA_1977__27_1_101_0 |
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Jul 19 |
comment |
What's the meaning of the general solution and the particular solution in differential equations? @Ron: added a small note about the non-linear case |
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Jul 19 |
revised |
What's the meaning of the general solution and the particular solution in differential equations? add note about non-linear equations |
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Jul 18 |
revised |
Hamilton-Jacobi Equation fix integration variables, add time as parameter to trajectories |
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Jul 18 |
comment |
Introduction to differential forms in thermodynamics @Arnold: I'll send you my list once I've done some further reading... |
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Jul 18 |
comment |
Introduction to differential forms in thermodynamics @Arnold: I started to read your book today (just the first chapter for now) and kept a list of typos/missing symbols, statements I find questionable etc; are you interested in that (ie should I keep adding to my list or stop now before investing any real work)? |
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Jul 18 |
comment |
Introduction to differential forms in thermodynamics @Arnold: your comment contains the quote "Infinitesimals and differential forms are the same thing, something well-known to mathematicians"; that seems to have been a typo, tough, if your argument is actually that differential forms and not infinitesimals are the correct framework for thermodynamics (which might indeed be the case - I don't know enough about non-standard analysis to be a judge of that) |
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Jul 18 |
comment |
Introduction to differential forms in thermodynamics @Ron: it doesn't? how do you interpret the legendre-transformation in terms of infinitesimals? |
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Jul 18 |
comment |
Introduction to differential forms in thermodynamics @Arnold: infinitesimals and differential forms are not the same thing; the framework of non-standard analysis got a rigorous set-theoretic formulation in the 70s and there are results which are indeed more easily formulated using infinitesimals; I'm not sure if non-standard analysis adds anything to thermodynamics in particular, though |
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Jul 18 |
revised |
Hamilton-Jacobi Equation added 6 characters in body |
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Jul 18 |
answered | What's the meaning of the general solution and the particular solution in differential equations? |
