Holomorphic Quantization of Linear Field Theory in the General Boundary Formulation

• Main Author: Robert Oeckl
• Format: Article
• Language: English
• Published: National Academy of Science of Ukraine 2012-08-01
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Subjects: geometric quantization; topological quantum field theory; coherent states; foundations of quantum theory; quantum field theory
• Online Access: http://dx.doi.org/10.3842/SIGMA.2012.050

We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the Kähler case, state spaces arise as spaces of holomorphic functions on linear spaces of classical solutions in neighborhoods of hypersurfaces. Amplitudes arise as integrals of such functions over spaces of classical solutions in regions of spacetime. We prove the validity of the TQFT-type axioms of the general boundary formulation under reasonable assumptions. We also develop the notions of vacuum and coherent states in this framework. As a first application we quantize evanescent waves in Klein-Gordon theory.