Quantum field theory on affine bundles

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. We also show the existence of a
functorial assignment of linear quantum field theories to affine ones. The
identification of suitable algebra homomorphisms enables us to induce
whole families of physical states (satisfying the microlocal spectrum
condition) for affine quantum field theories by pulling back quasi-free
Hadamard states of the underlying linear theories.