Linking the Gauss-Bonnet-Chern Theorem, Essential Hopf Maps and Membrane Solitons with Exotic Spin and Statistics

  • Chia-Hsiung Tze
Part of the NATO ASI Series book series (NSSB, volume 245)


By way of the Gauss-Bonnet-Chern theorem, we present a higher dimensional extension of Polyakov’s regularization of Wilson loops of point solitons. Spacetime paths of extended objects become hyper-ribbons with self-linking, twisting and writhing numbers. Specifically we discuss the exotic spin and statistical phase entanglements of geometric n-membrane solitons of D-dimensional KP 1 σ-models with an added Hopf-Chern-Simons term where (n, D, K) = (0, 3, C), (2, 7, H), (6, 15, Ω). They are uniquely linked to the complex (C) and quaternion (H) and octonion (Ω) division algebras.


Wilson Loop Division Algebra Statistic Connection Topological Quantum Field Theory Spacetime Path 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Chia-Hsiung Tze
    • 1
  1. 1.Department of Physics, Virginia TechInstitute of High Energy PhysicsBlacksburgUSA

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