Linear bosonic and fermionic quantum gauge theories on curved spacetimes

Abstract

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

28 pages, no figures; v2: svjour3 style, 24 pages, compatible with version to be published in General Relativity and Gravitation

References in corpus (10)

• The generally covariant locality principle -- A new paradigm for local quantum physics
• Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
• Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions
• Renormalized Quantum Yang-Mills Fields in Curved Spacetime
• A Quantum Weak Energy Inequality for Spin-One Fields in Curved Spacetime
• The extended algebra of observables for Dirac fields and the trace anomaly of their stress-energy tensor
• Classical and Quantum Fields on Lorentzian Manifolds
• Quantization of the Maxwell field in curved spacetimes of arbitrary dimension
• Quantization of the massive gravitino on FRW spacetimes
• Cauchy Problem and Green's Functions for First Order Differential Operators and Algebraic Quantization

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• Local and gauge invariant observables in gravity
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• The Calabi complex and Killing sheaf cohomology
• Linear Yang-Mills theory as a homotopy AQFT
• Dynamical locality of the free Maxwell field
• Quantization of the linearised Einstein-Klein-Gordon system on arbitrary backgrounds and the special case of perturbations in Inflation
• Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime
• Approaches to linear local gauge-invariant observables in inflationary cosmologies
• Snowmass White Paper: The Quest to Define QFT
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• Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
• Supergeometry in locally covariant quantum field theory
• On Maxwell's Equations on Globally Hyperbolic Spacetimes with Timelike Boundary
• Green hyperbolic complexes on Lorentzian manifolds
• The Quantization of Maxwell Theory in the Cauchy Radiation Gauge: Hodge Decomposition and Hadamard States
• On the uniqueness of invariant states