Linear bosonic and fermionic quantum gauge theories on curved spacetimes

Understand

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.