3,767 research outputs found

    Beyond the Frenkel-Kac-Segal construction of affine Lie algebras

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    This contribution reviews recent progress in constructing affine Lie algebras at arbitrary level in terms of vertex operators. The string model describes a completely compactified subcritical chiral bosonic string whose momentum lattice is taken to be the (Lorentzian) affine weight lattice. The main feature of the new realization is the replacement of the ordinary string oscillators by physical DDF operators, whereas the unphysical position operators are substituted by certain linear combinations of the Lorentz generators. As a side result we obtain simple expressions for the affine Weyl translations as Lorentz boosts. Various applications of the construction are discussed.Comment: 6 pages, LaTeX209 with twoside, fleqn, amsmath, amsfonts, amssymb, amsthm style files; contribution to Proceedings of the 30th Int. Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, Germany, August 27-31, 199

    Introduction to Vertex Algebras, Borcherds Algebras, and the Monster Lie Algebra

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    The theory of vertex algebras constitutes a mathematically rigorous axiomatic formulation of the algebraic origins of conformal field theory. In this context Borcherds algebras arise as certain ``physical'' subspaces of vertex algebras. The aim of this review is to give a pedagogical introduction into this rapidly-developing area of mathemat% ics. Based on the machinery of formal calculus we present the axiomatic definition of vertex algebras. We discuss the connection with conformal field theory by deriving important implications of these axioms. In particular, many explicit calculations are presented to stress the eminent role of the Jacobi identity axiom for vertex algebras. As a class of concrete examples the vertex algebras associated with even lattices are constructed and it is shown in detail how affine Lie algebras and the fake Monster Lie algebra naturally appear. This leads us to the abstract definition of Borcherds algebras as generalized Kac-Moody algebras and their basic properties. Finally, the results about the simplest generic Borcherds algebras are analysed from the point of view of symmetry in quantum theory and the construction of the Monster Lie algebra is sketched.Comment: 55 pages, (two minor changes thanks to comment by R. Borcherds

    Universal simple current vertex operators

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    We construct a vertex operator realization for the simple current primary fields of WZW theories which are based on simply laced affine Lie algebras g. This is achieved by employing an embedding of the integrable highest weight modules of g into the Fock space for a bosonic string compactified on the weight lattice of g. Our vertex operators are universal in the sense that a single expression for the vertex operator holds simultaneously for all positive integral values of the level of g.Comment: 17 pages, LaTeX2

    Ultra-Wide Swath SAR Imaging With Continuous PRF Variation

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    Innovative multi-channel synthetic aperture radar (SAR) concepts enable high-resolution wide-swath imaging, but the antenna length typically restricts the achievable swath width. This limitation can be overcome by a novel technique which is based on a single azimuth channel but operates the system with a continuously varied pulse repetition frequency (PRF) by this allowing in principle for arbitrary wide swaths. This paper introduces the basic principles and discusses design constraints for such a PRF variation. Further, a systematic performance analysis of an L-band reflector antenna system is carried out with focus on the sensitivity versus different input parameters

    Explicit determination of a 727-dimensional root space of the hyperbolic Lie algebra E10E_{10}

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    The 727-dimensional root space associated with the level-2 root \bLambda_1 of the hyperbolic Kac--Moody algebra E10E_{10} is determined using a recently developed string theoretic approach to hyperbolic algebras. The explicit form of the basis reveals a complicated structure with transversal as well as longitudinal string states present.Comment: 12 pages, LaTeX 2
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