Mathematical Aspects of Quantum Field Theories pp 275-324 | Cite as

# Semiclassical Quantization of Classical Field Theories

## 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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