Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-04-28
J. Geom. Phys. 62 (2012) 1373-1396
Physics
High Energy Physics
High Energy Physics - Theory
42 pages, LaTeX + AMS; v2: expanded to improve readability, new sections 3.1 (geometric data) and 3.3 (core axioms), minor cor
Scientific paper
10.1016/j.geomphys.2012.02.001
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation, allowing to implement manifest locality without the necessity for metric or causal background structures. The quantization combines the holomorphic version of geometric quantization for state spaces with the Feynman path integral quantization for amplitudes. We also develop an adapted notion of coherent states, discuss vacuum states, and consider observables and their Berezin-Toeplitz quantization. Moreover, we derive a factorization identity for the amplitude in the special case of a linear field theory modified by a source-like term and comment on its use as a generating functional for a generalized S-matrix.
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