The use of rigorous mathematical techniques to make new predictions and test the limits and validity of physical models, while also developing new techniques in mathematics.

• Raul Alvarez

  Hi everyone, I would like to ask for some references for "cohomological field theories"

  I'm trying to understand the concept of twisting that arises in the context of topological quantum field theory of cohomological type. I'm not a true physicist, so all the references I've got so farI'm trying to understand the concept of twisting that arises in the context of topological quantum field theory of cohomological type. I'm not a true physicist, so all the references I've got so far are quite obscure to me. I would like (I need, to be honest) a more mathematically precise definition of the concept of "topological twisting" in order to understand better the physical meaning. I really appreciate your comments as well as your references. Greetings Raúl

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    Carlos Lozano replied

    The basic idea concerning "obstructions" is similar to the introduction of spinc structures to overcome the obstruction to defining spinors on non-spin manifolds. In short, rigid supersymmetry onThe basic idea concerning "obstructions" is similar to the introduction of spinc structures to overcome the obstruction to defining spinors on non-spin manifolds. In short, rigid supersymmetry on curved spaces requires covariantly constant spinors \epsilon. That is to say, you get an equation like (\partial_\mu+\omega_\mu)\epsilon = 0 where \omega_\mu is the spin connection. What twisting does is essentially to add an additional connection h_\mu to the above equation (by "gauging" the global R-symmetry group of the supersymmetric theory) in such a way that you compensate the \omega_\mu part (=you couple the \omega_\mu = holonomy transformation to the h_\mu = R-symmetry transformation so that their action on \epsilon is trivial so that the condition is only \partial_\mu \epsilon = 0 ). So when you move around (=parallel transport) the resulting "twisted" spinor around a closed loop you have to transform it with \omega_\mu + h_\mu (which is = 0 because you have defined the coupling to do so) so, in effect, you get something with different holonomy properties (i.e. different spins). The idea of realizing twisted theories as supersymmetric theories on certain special holonomy manifolds that I mentioned in my previous post arose in http://arxiv.org/pdf/hep-th/9511222v1.pdf, where there is a detailed discussion concerning twists of the N=4 theory.

    Apr 26, 2012
• Sachin Kumar

  How we can derive the Differential equations from the metric form?

  For example Einstein field equations are in metric form. How we can derive the differential equations from the Einstein field equations in the metric form? Is there any book on this topic? To make myFor example Einstein field equations are in metric form. How we can derive the differential equations from the Einstein field equations in the metric form? Is there any book on this topic? To make my question clear i am attaching a link of a paper. Please see it. In this paper author has obtained the Einstein field equations in the form partial differential equations. I am not able to understand how she has derived these equations form the above equations in that paper. My question is "How other Einstein equations can be derived in form of partial differential equations?"

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    Sachin Kumar replied

    Thanks a lot for your reply. I will try the steps you have explained. Can you please suggest me some book or article where i can find a simple examples related to this topic? I shall be very thankfulThanks a lot for your reply. I will try the steps you have explained. Can you please suggest me some book or article where i can find a simple examples related to this topic? I shall be very thankful of you.

    Apr 25, 2012
• Francisco Flores

  Experimental tests for string theory

  I am an undergraduated student and I have heard that string theory is a beautiful framework for a theory of everything but it seems to have a little problem, the theory is very hard to prove by anI am an undergraduated student and I have heard that string theory is a beautiful framework for a theory of everything but it seems to have a little problem, the theory is very hard to prove by an experiment, so, my question is the following: Does exist at least an experiment proposed to test the theory? No matter if the technology of today is not able to let us test the theory, but at least would be nice to have a proposed experiment for the physicists of the next generations. If this exists I would appreciate the reference.

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    Brandon Johnson replied

    I saw a post on reddit (subsequently lost) that basically said string theory is looking more unlikely as a candidate. By "covering over" I mean that the Planck length is the "width" of a string, butI saw a post on reddit (subsequently lost) that basically said string theory is looking more unlikely as a candidate. By "covering over" I mean that the Planck length is the "width" of a string, but without discussing what is inside the loop itself. If there is a "loop", the loop has a "center". Why discuss the loop and not the center - what's "inside" the loop? Personally, I think that relativity, as well as quantum mechanics, is so misunderstood because of the number zero, and it's being tied to infinity - A PL loop would equal both zero size and infinite size at the same time. Infinitesimal calculus is flawed here, and can't do much more than approximate everything. As for Sir Penrose, I know he pursues several "unpopular" or "unworkable" theories, but I share his thoughts; If we had a ToE, then I would be working on it, but we don't, so I'm still exploring all options available to me. Why not explore all the ideas that sound good? I am even working on my own ToE, from an idea I had just before new years last year, and it's holding up to special and general relativity, as well as string theory and QED/QCD. I think I know what the Higgs field is, and why symmetry breaking occurs with the Higgs, but my theory is useless without a test, and the test is my machine - I intend to build a machine that actually circumvents thermodynamics and produces 1836x more output than input.

    Apr 16, 2012
• Rob Carroll

  Could the distribution of the prime numbers be related to a physical system?

  It seems that the distribution of eigenvalues in quantum chaotic systems obeys the same statistics as eigenvalues of random matrices. e.g.It seems that the distribution of eigenvalues in quantum chaotic systems obeys the same statistics as eigenvalues of random matrices. e.g. http://www.researchgate.net/publication/51969774_Generalized_random_matrix_conjecture_for_chaotic_systems It has also been shown that the distribution of the critical zeros of the Riemann zeta-function can be related to the distribution of eigenvalues of certain random matrices: http://www.researchgate.net/publication/51940315_Random_matrices_and_Riemann_hypothesis So this would seem to to suggest a statistical relationship between the zeros of the zeta function and the energy levels some quantum chaotical system. Can any relationship be drawn between the placement of the prime numbers and a dynamical system? Any other implications of this connection?

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    Sanjay Sood replied

    Rob, you are asking a very good question. If this question could be answered, it not only shed light on the nature of the behavior of chaotic quantum system which is analytically intractable and theRob, you are asking a very good question. If this question could be answered, it not only shed light on the nature of the behavior of chaotic quantum system which is analytically intractable and the nature of the distribution of the roots of Riemann Zeta function.

    Apr 4, 2012
• Hugo Vercammen

  In the set of Gell-Mann matrices: why is L8 not {L8(2,2)=-L8(3,3)=1 and all other L8(i,j)=0}?

  Would this not give a simpler and more uniform definition without the awkward sqrt(3)?

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    Hugo Vercammen replied

    Looking further into it I find that L3 and L8 are not trace orthogonal. Is this a problem? What are the consequences?

    Feb 16, 2012