A History of Mathematical Notations: Vol. I, Notations in by Florian Cajori

By Florian Cajori

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B 340, 33. , R. G. Leigh, and J. Polchinski, 1989, Mod. Phys. Lett. A 4, 2073. Danielsson, U. , and G. Ferretti, 1997, Int. J. Mod. Phys. A 12, 4581. , H. Nicolai, and J. Plefka, 2000, J. High Energy Phys. 05, 007. de Alwis, S. , 1999, Phys. Rev. D 59, 044029. , K. Hori, and H. Ooguri, 1998, Nucl. Phys. B 525, 257. , S. Panda, and J. P. van der Schaar, 1998, Phys. Lett. B 426, 50. , 1999, ‘‘Supermembranes and super matrix models,’’ preprint hep-th/9902051. , J. Hoppe, and H. Nicolai, 1988, Nucl.

We have described two complementary ways of thinking about matrix theory: first, as a quantized regularized theory of a supermembrane, which can be interpreted as a second-quantized theory of objects moving in an 11-dimensional target space, and second, as the discrete light-cone quantization of M theory, which is equivalent to a simple limit of type-IIA string theory through the Seiberg-Sen limiting argument. We have reviewed perturbative matrix-theory calculations that correspond precisely with linearized 1114 See, for example, Balasubramanian, Gopakumar, and Larsen (1998), Hyun (1998), Itzhaki et al.

448 Washington Taylor: M(atrix) theory corresponds to longitudinal membranes (strings), the charge z ij ϳJ ϩij ϳϪiTr ͓ X i ,X j ͔ (134) corresponds to transverse membranes, and z ijkl ϳM ϩϪijkl ϳTr X [i X j X k X l] (135) corresponds to the longitudinal M5-brane charge. Yet another way to motivate these charge identifications is through T duality in the type-IIA picture. This approach is described by Taylor (1998, 2000), Taylor and Van Raamsdonk (1999a), and Myers (1999). The perturbative matrix-theory calculations described in Sec.

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