Linear bosonic and fermionic quantum gauge theories on curved spacetimes

• Published in: General relativity and gravitation Vol. 45; no. 5; pp. 877 - 910
• Main Authors: Hack, Thomas-Paul, Schenkel, Alexander
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.05.2013
• Subjects: Astronomy; Astrophysics and Cosmology; Classical and Quantum Gravitation; Differential Geometry; Editor’s Choice (Research Article); Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Theoretical; Quantum field theory on curved spacetimes; Algebraic quantum field theory; Gauge theories; Supergravity
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-013-1508-y

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 linearised Yang-Mills theory and linearised 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 linearised pure 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.