Edge-of-the-wedge theorem

In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum field theory to construct the analytic continuation of Wightman functions. The formulation and the first proof of the theorem were presented[1][2] by Nikolay Bogoliubov at the International Conference on Theoretical Physics, Seattle, USA (September, 1956) and also published in the book Problems in the Theory of Dispersion Relations.[3] Further proofs and generalizations of the theorem were given by Res Jost and Harry Lehmann (1957),[4] Freeman Dyson (1958), H. Epstein (1960), and by other researchers.

  1. ^ Vladimirov, V. S. (1966), Methods of the Theory of Functions of Many Complex Variables, Cambridge, Mass.: M.I.T. Press
  2. ^ V. S. Vladimirov, V. V. Zharinov, A. G. Sergeev (1994). "Bogolyubov's “edge of the wedge” theorem, its development and applications", Russian Math. Surveys, 49(5): 51—65.
  3. ^ Bogoliubov, N. N.; Medvedev, B. V.; Polivanov, M. K. (1958), Problems in the Theory of Dispersion Relations, Princeton: Institute for Advanced Study Press
  4. ^ Jost, R.; Lehmann, H. (1957). "Integral-Darstellung kausaler Kommutatoren". Nuovo Cimento. 5 (6): 1598–1610. Bibcode:1957NCim....5.1598J. doi:10.1007/BF02856049. S2CID 123500326.