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Abstract
The ColemanMandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result
for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity.
Unlike the CM theorem, our result is valid in dimensions n≥2 and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group G on the category of spacetimes.
Such symmetries are shown to be canonically associated with a cohomology class
in the second degree nonabelian cohomology of G with coefficients in the global
gauge group of the theory. Our main result proves that the cohomology class is trivial if G is the universal cover S of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and S, all fields transform in multiplets of S, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance.
for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity.
Unlike the CM theorem, our result is valid in dimensions n≥2 and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group G on the category of spacetimes.
Such symmetries are shown to be canonically associated with a cohomology class
in the second degree nonabelian cohomology of G with coefficients in the global
gauge group of the theory. Our main result proves that the cohomology class is trivial if G is the universal cover S of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and S, all fields transform in multiplets of S, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance.
Original language  English 

Pages (fromto)  353–378 
Number of pages  26 
Journal  Communications in Mathematical Physics 
Volume  357 
Issue number  1 
Early online date  19 Jul 2017 
DOIs  
Publication status  Published  Jan 2018 
Bibliographical note
© The Author(s) 2017.Profiles

An analogue of the ColemanMandula theorem for QFT in curved spacetimes
Chris Fewster (Invited speaker)
8 Mar 2017Activity: Talk or presentation › Invited talk

Operator Algebras and Quantum Field Theory. Dedicated to the Memory of John E. Roberts.
Chris Fewster (Invited speaker)
27 Jun 2016 → 29 Jun 2016Activity: Participating in or organising an event › Conference participation