The Quantum Geometry of Polyhedral Surfaces

  • Mauro Carfora
  • Annalisa Marzuoli
Part of the Lecture Notes in Physics book series (LNP, volume 845)


Among the many significant ideas and developments that connect Mathematics with contemporary Physics one of the most intriguing is the role that Quantum Field Theory (QFT) plays in Geometry and Topology. We can argue back and forth on the relevance of such a role, but the perspective QFT offers is often surprising and far reaching. Examples abound, and a fine selection is provided by the revealing insights offered by Yang–Mills theory into the topology of 4-manifolds, by the relation between Knot Theory and topological QFT, and most recently by the interaction between Strings, Riemann moduli space, and enumerative geometry. Doubtless many of the most striking connections suggested by physicists failed to pass the censorship of the Department of Mathematics, and so do not appear in the above official list. As ill-defined these techniques may be, if we give them some degree of mathematical acceptance then the geometrical perspective they afford is always quite non-trivial and extremely rich. It is within such a framework that we shall examine in this and following chapters some aspects of the relation between an important class of QFTs and polyhedral surfaces. We start with a rather general introduction on geometrical aspects of QFT that will allow us to introduce naturally a notion of Quantum Geometry.


Modulus Space Riemann Surface Hyperbolic Surface Ribbon Graph Polyhedral Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mauro Carfora
    • 1
  • Annalisa Marzuoli
    • 1
  1. 1.Dipto. Fisica Nucleare e TeoricaIstituto Nazionale di Fisica Nucleare e Teorica, Sez. di Pavia, Università degli Studi di PaviaPaviaItaly

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