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I've been wondering about the definition of Quantum Fields in Curved Space-times (CS). I know that, in flat space-time (Minkowski), the fields are defined as irreducible representations of the universal covering group SU(2)xSU(2) of SO(4) (which is basically the Lorentz group SO(1,3) under a Wick rotation of time).

Nevertheless, in general (that is in CS) your field theory is not invariant under Lorentz transformations. How then are fields defined in CS? Could you explain your answer and give some references, please?

Thanks

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# Quantum Fields in Curved Space-times

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