Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold (\\\"phase space\\\"). His algorithm gives a non-commutative, but associative, product (a so-called \\\"star-product\\\") between smooth phase space functions parameterized by Planck\\\'s constant ℏ, which is treated as a deformation parameter. In the limit as ℏ goes to zero, the star product commutator goes to ℏ times the Poisson bracket, so in this sense his method provides a quantization of the algebra of classical observables. In this work, we develop a generalization of Fedosov\\\'s method which applies to the infinite-dimensional symplectic \\\"manifolds\\\" that occur in Lagrangian field theories. We show that the procedure remains mathematically well-defined, and we explain the relationship of this method to more standard perturbative quantization schemes in quantum field theory.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-224698 |
| Date | 11 May 2017 |
| Creators | Collini, Giovanni |
| Contributors | Universität Leipzig, Fakultät für Physik und Geowissenschaften, Prof. Dr. Stefan Hollands, Prof. Dr. Stefan Waldmann, Prof. Dr. Stefan Hollands |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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