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Semiclassical Quantization of Classical Field Theories

  • Alberto S. CattaneoEmail author
  • Pavel Mnev
  • Nicolai Reshetikhin
Chapter
Part of the Mathematical Physics Studies book series (MPST)

Abstract

These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in the usual Hamiltonian framework. Then we outline formal semiclassical quantization in the finite dimensional case. Towards the end we give an example of such a quantization in the case of Abelian Chern-Simons theory.

Notes

Acknowledgments

The authors benefited from discussions with T. Johnson-Freyd, J. Lott and B. Vertman, A.S.C. acknowledges partial support of SNF Grant No. 200020-131813/1, N.R. acknowledges the support from the Chern-Simons grant, from the NSF grant DMS-1201391 and the University of Amsterdam where important part of the work was done. P. M. acknowledges partial support of RFBR Grant No.13-01-12405-ofi-m-2013, of the Chebyshev Laboratory (Department of Mathematics and Mechanics, St. Petersburg State University) under RF Government grant 11.G34.31.0026, of JSC “Gazprom Neft”, and of SNF Grant No. 200021-13759. We also benefited from hospitality and research environment of the QGM center at Aarhus University.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Alberto S. Cattaneo
    • 1
    Email author
  • Pavel Mnev
    • 2
    • 3
  • Nicolai Reshetikhin
    • 4
    • 5
    • 6
  1. 1.Institut Für MathematikUniversität ZürichZürichSwitzerland
  2. 2.St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of SciencesSt. PetersburgRussia
  3. 3.Chebyshev LaboratorySt. Petersburg State UniversitySt. PetersburgRussia
  4. 4.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  5. 5.KdV Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  6. 6.ITMO UniversitySaint PetersburgRussia

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