Quantum field theory on affine bundles

Understand

We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes.

• All concepts and results are formulated using the language of category theory, which allows us to prove that these models satisfy the principle of general local covariance.
• Our analysis is a preparatory step towards a full-fledged quantization scheme for the Maxwell field, which emphasises the affine bundle structure of the bundle of principal U(1)-connections.
• As a by-product, our construction provides a new class of exactly tractable locally covariant quantum field theories, which are a mild generalization of the linear ones.