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By Blackburn Ch. M.

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Extra resources for An Application of the Quantum Theory of Band Spectra to the First Negative Deslandres Group of Carbon

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1. Two-dimensional Minkowski space is conformally mapped into the interior of the rectangle. Fig. 2. The rectangular region can be embedded in a cylinder, with " and "! being identi"ed. @  J , and generate the maximally compact subgroup SO(2);SO(2) of SO(2, 2). 13) N\ where d is the line element on the unit sphere SN\. u )d  (u "t$r) > \  > \ N\ ! u )d  ) (u "tan u ) " > \  > \ N\ ! d #d #sin d  ) (u "( $ )/2) . 14) N\ ! 4 cosu cosu > \ As shown in Fig. 3, the (t, r) half-plane (for a "xed point on SN\) is mapped into a triangular region in the ( , ) plane.

We can expand the bulk action as a free quadratic part describing the propagation of free massless modes (including the graviton), plus some interactions which are proportional to positive powers of the square root of the Newton constant. 2) where we have written the metric as g" # h. We indicate explicitly the dependence on the graviton, but the other terms in the Lagrangian, involving other "elds, can be expanded in a similar way. Similarly, the interaction Lagrangian S is proportional to positive powers of .

3) containing the asymptotic region [149]. 3), since the superconformal algebra has twice as many fermionic generators as the corresponding Poincare superalgebra. We also have an SO(6) symmetry which rotates the S. This can be identi"ed with the S;(4) R-symmetry 0 group of the "eld theory. In fact, the whole supergroup is the same for the N"4 "eld theory and the AdS ;S geometry, so both sides of the conjecture have the same spacetime symmetries. 2. 1 that we could also think of the conformal "eld theory as de"ned on S;1 by rede"ning the Hamiltonian.

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An Application of the Quantum Theory of Band Spectra to the First Negative Deslandres Group of Carbon by Blackburn Ch. M.


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