A student wanted me to help him with some homework. So I agreed, he said he was a undergraduate from Iowa State. And then I saw the homework. OH MEIN GOTT!!! Listen to some of these questions Can we prove new theorems in geometry and new constraints on consistent theories of gravity using techniques of 2d CFT? Does space time look non communitive or non associative at the Planckian string scale and if yes what does this imply form gravity? Is there an example of non supersymmetric intergrable string model with an interesting 4d target space interpretation? I thought my head was going to explode! These arent undergraduate questions. So I told him...the first one deals with the AdS/CFT correspondence. This is basically a really really advanced version of quantum field theory. In the AdS/CFT correspondence, you have to interdisciplinarily combine string theory or M-theory on an anti-de Sitter background. The geometry of spacetime is described in terms of a certain vacuum solution of Einsteins equation (usually the cosmological constant) called anti-de Sitter space. In more detail the anti-de Sitter space is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. It is the Lorentzian analogue of a non-Euclidean geometry n-dimensional hyperbolic space, just as Minkowski space and de Sitter space are the analogues of Euclidean and elliptical spaces respectively. I wouldnt have even know about this if I hadnt watched this lecture on loop quantum gravity from the SETI Institute. Question number 10 deals with Noncommutative geometry....which is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions. I just started studying that a month ago with these classes from Poland. Question number 20 deals with Global supersymmetry and superparticles. Wigner-Weyl theory is something to look into for this and it is in ordinary quantum field theory that unitary representations of the Poincaré group correspond to the particles in the theory. For a globally supersymmetric quantum field theory the Poincaré group here is replaced by the super Poincaré group and accordingly particles are now irreducible representations of this group: the irreducible unitary representations of the super Poincaré group. The new – odd graded – pieces of these representations – called supermultiplets – appearing this way are called the superpartners of the original bosonic particles. Question 30 deals with How Time ‘Emerges’ from Quantum Entanglement and the Wheeler-DeWitt equations.
Posted on: Mon, 14 Jul 2014 15:08:20 +0000
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