Poincare Definition and 139 Threads

We call a group G "simply connected" if every curve C(t) in G which is closed (that is, C(0) = C(1) = I) can be continuously deformed into the trivial curve C'(t) = I (where I is the unit element in G). This is formalised saying that, for each closed C(t), there exists a continuous function F...

Not sure if this is the right place to ask, but this doubt originated when reading on string theory and so here it goes... The general canonical energy-momentum tensor (as derived from translation invariance), T^{\mu\nu}_{C} is not symmetric. Also, the general angular momentum conserved...

Generally we say GR is local Lorentz invariant. Does it mean the action or field equation? Why not Poincare invariant? Thanks!

Hi, Can someone explain the concept of "Poincare sphere"? What's the relationship between the Poincare Sphere and the Degree of polarization of EM fields? Thanks Madara

Does anyone know what a matrix representation of the poincare group generators looks like (specifically the translation parts)? I've been trying to figure this out but I get matrices that are dependent on the group parameters.

Never mind, I answered my own question...

I am facing a dilemma which leaves me quite puzzled. I hope someone can straighten this out. The short version is : when we use representations of the charges as differential operators to calculate their commutators, we always get -1 times the correct result. So, doe sthat mean that we...

Incidence Postualte I-1 holes for the Poincare Model: Every two points of E lie on exactly one L-Line. Prove: Given any two points P and Q inside the unit circle C, there exists a unique L-line l containing them. (this will require the use of analytic geometry.) L-lines:arcs of circles...

Homework Statement Find the commutators [P^\sigma,J^{\mu \nu}] The answer is part of the Poincare algebra [P^\sigma,J^{\mu \nu}]=i(g^{\mu \sigma}P^\nu-g^{\nu \sigma}P^\mu) If someone can convince me that \partial_i T^{0\mu} = 0, (i.e. the energy-momentum tensor has no explicit spatial...

It's notable that Poincaré many years before Einstein had very interesting ideas on the constancy of light. For example: In his paper http://en.wikisource.org/wiki/The_Measure_of_Time" Poincaré wrote in 1898: Abraham Pais (in Subtle is the Lord) said that "These lines read like the general...

If we have a system for which the Liouville's tm holds, can we automaticly say the Poincare's recurrence tm also holds? Presumably this is true in microcanonical ansable, but how about canonical, where the energy isn't constant?

Just a quick question here: I was going through my notes and I noticed that the generators of both these groups are labeled two indices. I was wondering if there is any particular reason for this, since it seems to me that one index would work perfectly well. Thanks

Hi I need to find the generators of the Poincare group in the representation of a clasical scalar field. Every textbook I found let them as P and M. But any buk does not what are they. I'm wondering if anybody help me to find this Uda

[SOLVED] poincare conjecture http://en.wikipedia.org/wiki/Solution_of_the_Poincar%C3%A9_conjecture The links to Perelman's original proof do not work. Can someone fix them please?

Ok first i'd like to note that I'm not good at mathematics and have a vague understanding of the conjecture. What i'd like to know though is what comes now that this has been solved by Perelman? What implications does this have?

Does the Poincare conjecture say: Consider a compact 3-dimensional manifold V without boundary. Poincare conjectured that The fundamental group of V is trivial => V is homeomorphic to the 3-dimensional sphere? It has been proved for all manifolds except 3. However Perelman completed a proof...

There is a work in history of astronomy I've been preparing for the most of the time in living memory. I can't say is it late, or due, or long, but counting from the 3 books I've seen, the one in focus of some private interest is Michael Hoskin "Cambridge Illustrated History of Astronomy"...

After a lot of searching I cannot for the life of me find the transformation for a Momentarily Co-moving Reference Frame. Essentially what I'm looking for is the transformations from inertial frame Sigma to inertial frame Sigma[']. Sigma['] is moving at speed v relative to Sigma not along any...

I recently studied supersymmetry breaking and read there that for Supersymmetry breaking we have the energy of the vacuum state >0. However what I do not really see is why such a vacuum would not break Poincare invariance as well as the energy is part of the momentum 4-vector and so transforms...

Dear all, I just received by mail the https://www.amazon.com/dp/0471925675/?tag=pfamazon01-20. I am very very happy. At each page I can see something new to learn. But I would like to learn a bit more about his remark on page 28. (you can read it with the amazon reader) He talks about...

What is the poincare conjecture in layman's terms?

Navier&Stokes to follow Poincare?? It seems that yet another important problem in mathematics, and more importantly in physics, may have been solved. This time it's the Navier-Stokes Equation. This, too, is on the Clay Mathematical Institute's list of Millenium Problems. I've seen a couple of...

After reading the article on Poincare's conjecture in the Economist, I became curious about simplified 3-dimensional objects. Excerpt: Let's take a cube and simplify it into a circle. Could we then use equations ment for circles for the simplified shape, ie calculate the cube's surface...

Derivation of Poincare Invariance from general quantum field theory C.D. Froggatt, H.B. Nielsen Annalen der Physik, Volume 14, Issue 1-3 , Pages 115 - 147 (2005) Special Issue commemorating Albert Einstein Starting from a very general quantum field theory we seek to derive Poincare...

Does anyone know of an accessible reference that sketches a proof of Poincare's recurrence theorem? (This is not a homework question.) I'm coming up short in my searches -- either the proof is too sketchy, or it is inaccessible to me (little background in maths, but enough to talk about...

Perelman, Poincare Conjecture solved now?? Seems that this guy has solved the Poincaré Conjecture: http://en.wikipedia.org/wiki/Grigori_Perelman He is supposed to get the Fields Medal in Madrid this year, in the next international congress of mathematics. But it is likely that he won't...

Announced in http://www.intlpress.com/AJM/p/2006/10_2/AJM-10-2-165-492.pdf" . Differential Geometry meets Geometric Surgery on three-manifolds; Perelman clarified and (perhaps) corrected. A COMPLETE PROOF OF THE POINCAR´E AND GEOMETRIZATION CONJECTURES – APPLICATION OF THE...

(I am not sure whether I'm posting in the right forum. I apologize if I do) Does anyone have an alrorithm or a code (in any language) that constructs a Poincare surface of section? I want to do so for a Hamiltonian model: A mass under the influense of the Henon-Heiles potential. It has to...

I am an MPhys graduate currently reading Joseph Polchinski’s, String Theory, Vol. 1. Unsurprisingly I’m stuck on the first real bit of maths… :p I quote from page 10, heh: “The simplest Poincaré invariant action that does not depend on the parametrization would be proportional to the proper...

I am an MPhys graduate currently reading Joseph Polchinski’s, String Theory, Vol. 1. Unsurprisingly I’m stuck on the first real bit of maths… :p I quote from page 10, heh: “The simplest Poincaré invariant action that does not depend on the parametrization would be proportional to the proper...

Could someone lay down, in layman's terms, The Poincare Conjecture? Lol, is this even possible?

Why isn't the mathematician Henri Poincaré acknowledged as the true discoverer of special relativity? http://www-cosmosaf.iap.fr/Poincare-RR3A.htm http://arxiv.org/abs/physics/0408077

Poincare Recurrence Theorem states that: "If a flow preserves volume and has only bounded orbits then for each open set there exist orbits that intersect the set infinitely often." But it does not imply (does it?) that "In hamiltonian system with bounded phase space, all trajectories will...

http://mathworld.wolfram.com/news/2003-04-15/poincare/ Is the proof considered valid? Did he claim the millennium prize? I can't find any recent news about it.

I do not know much about string theory, but the fact that it involves 10 or 11 dimensions. I am curious whether this 10 or 11 dimensions of string theory has anything to do with inhomogenous lorentz transformation?. ---- [from Goldstein - section 7-2] In essence a poincare...

I just read the latest Scientific American and they have an article about the proof of the Poincaré conjecture. Apparently the proof uses a modified (an extra element) Ricci flow and then the article says that the modification to the Ricci flow pops up in Super String Theory :confused: ...

Are there any updates on this? I don't know how old this is, but I am curious. I thought it was pretty interesting stuff. -------The Poincare Conjecture, one of the most famous math problems solved A Russian mathematician claims to have proved the Poincare Conjecture, one of...

Mathematicians are now saying that Grigory Perelman has really solved the conjecture and the proof will be in a paper he will post in the near future. His previous papers on this subject are in the arxiv specal topic Differential Geometry (under mathematics). Keep your eyes on this space!

The New York Times did an article today about a Russian mathemetician who claims to have proved the Poincare Hypothesis. In good Andrew Wiles fashion his proof is actually much further reaching results with the actuall proof of Poincare's Hypothesis dropping out of the larger result. Thought...