Affine holomorphic quantization

Understand

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.