Quantum field theory on affine bundles

Abstract

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.

34 pages, no figures; v2: 35 pages, compatible with version to be published in Annales Henri Poincare

References in corpus (4)

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• Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes

Cited by in corpus (9)

• Quantum Field Theory on Curved Backgrounds -- A Primer
• Electromagnetism, local covariance, the Aharonov-Bohm effect and Gauss' law
• A C*-algebra for quantized principal U(1)-connections on globally hyperbolic Lorentzian manifolds
• Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states
• Dynamical locality of the free Maxwell field
• Locally covariant quantum field theory with external sources
• Abelian duality on globally hyperbolic spacetimes
• Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
• The Casimir effect from the point of view of algebraic quantum field theory