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Jul
16
revised Smooth trajectory on a smooth manifold
added 471 characters in body
Jul
16
answered Smooth trajectory on a smooth manifold
Jul
15
comment What are some mechanics examples with a globally non-generic symplecic structure?
My motivation is really to find out if the mathematical definition in that approach is over the top. Even if the physical problems motivated the mathematical studies and the discovery of the extension and embedding in the elaborate differential geometric picture with its possibilities ...it's not necessary to use the full (mathematical) Hamiltonian system formalism in the definition, if it gets never ever used.
Jul
15
comment What are some mechanics examples with a globally non-generic symplecic structure?
Okay, the torus example as compactification is not so interesting per se, i.e. without stating an actual form which makes physical sense (since the canonical form would again be the first idea here). But I see that from that statement about 2-dim manifolds, there is $S^2$ and you probably have to have some more complicated form there, maybe $\sin(\vartheta)\ \text d \phi\wedge\text d\vartheta$ or so. Any actual mechanical problem in mind?
Jul
15
revised What are some mechanics examples with a globally non-generic symplecic structure?
added 136 characters in body
Jul
15
asked What are some mechanics examples with a globally non-generic symplecic structure?
Jul
15
comment shifting from mathematics to physics
@RonMaimon: Hey Ron, what do you charge for some lessons :D (Sadly, I'm not anywhere near NYC)
Jul
13
answered Is this a valid understanding of Newtonian mechanics?
Jul
13
comment Is this a valid understanding of Newtonian mechanics?
What is they in the first sentence? The equations of motion? And what does merely stating three laws mean, I guess you have to state some laws eighter way. And why is stating the equations of motion not elegant? You say they arise from the Noether theorem over the course of symmetries, but is there really an argument for what comes before what? You have to postulate some Lagrangian in both cases. In any case, I agree that the more recent ways of putting mechanics are pretty elegant.
Jul
13
comment Please explain me how the Higgs boson gives mass to other particles, more detail?
Have you made up your mind on what "mass" of a particle means to you in that question? Maybe that will help.
Jul
12
comment What is the minimal set of expectation values I need in a statistical model?
+1 Thanks for the elaboration regarding the uniqueness of function expectations by their moments. I guess I know how to integrate via substitutation, so I'm not necessarily "bothered" by it (as the bounds are $0$ and $\infty$, that identity $\int E^{n-1}f(E/T)dE=c T^n$ is true by dimentional arguments already). I guessed collecting fourier transformation data will be sufficient by the fact that Fourier transform spectroscopy etc is possible. In fact, the question was also motivated by the fact that I'm intimidated (not bothered) by other integrals sucking out information, e.g. Radon transform.
Jul
12
comment What is the minimal set of expectation values I need in a statistical model?
@RonMaimon: In the Gamma case, i.e. Laplace transform, the property of getting simple powers of the temperature and the fact that taylor series happen to use these as basis makes me think that for the exponential functions, basically any function space basis is a valid one to study and thereby know the whole system at one. Here the question is if there are rules to deduce that from the property of f. Then there is the second point if these kind of "basis for measruement space" property gets lost in a noncommutative system. I mean knowning <X> and <P> will in general not help you with <H(P,X)>.
Jul
12
revised What is the minimal set of expectation values I need in a statistical model?
added 36 characters in body
Jul
12
asked What is the minimal set of expectation values I need in a statistical model?
Jul
11
comment Standard notation reference
@DavidZaslavsky: That's funny, all the questions I really would want an answer to (questions I'd not be able to answer by reading the right books/articles) are "soft" or meta questions.
Jul
11
revised List of Physical Toys
added 299 characters in body
Jul
11
answered List of Physical Toys
Jul
11
comment Will adding heat to a material increase or decrease entropy?
Either one reads this statement as equivalent to the formula in Rons answer, or it's just not true (e.g. if one considers adiabatic compression).
Jul
11
comment The Dirac Equation with a 6x6 Matrix
Going in the direction of David BarMoshe's answer, this free book on fields by Warren Siegel covers some of the math around page $129\pm 20$.
Jul
11
comment Laplace operator's interpretation
@PeterMorgan: As the number of physics.SE users is manageable, the credit points seem like a useless or at least unused resource. The number of featured threads is also strangely small here, compared to say the math board where they have always 5-15 featured questions. I can sit on 3500 points, or I'll use them for bumping an interesting thread. The rate I get points is predictable and I'll have 500 once I actually need them. Also, I was hoping someone would start ranting about codifferentials and friends. Lastly, I want to know if I can go marble cake also the game on users pages.