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Index formulas for generalized Wiener-Hopf operators and boson-fermion correspondence in 2N dimensions

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Abstract

The kernels of operators associated with special chiral gauge transformations (‘kinks’) in the 2N-dimensional Dirac theory are explicitly determined. The result is used to obtain index formulas for Fredholm operators corresponding to continuous chiral gauge transformations. Moreover, the Fock space quadratic forms corresponding to the kinks are proved to converge to the Dirac field as the kink size goes to zero. It is also shown that forN ≡1, 2(mod 4) the Majorana field can be reached in a similar fashion.

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science, P.O. Box 4079, NL-1009 AB, Amsterdam, The Netherlands

    S. N. M. Ruijsenaars

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  1. S. N. M. Ruijsenaars
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Communicated by A. Connes

Work supported by the Netherlands Organisation for the Advancement of Research (NWO)

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Ruijsenaars, S.N.M. Index formulas for generalized Wiener-Hopf operators and boson-fermion correspondence in 2N dimensions. Commun.Math. Phys. 124, 553–593 (1989). https://doi.org/10.1007/BF01218451

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  • DOI: https://doi.org/10.1007/BF01218451

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