A covariant signature change from Euclidean to Lorentzian geometry on a curvature-regular hypersurface generates inflation via an effective geometric stress tensor, with duration set by the interpolator slope relative to extrinsic and spatial curvatures.
How to Wick rotate generic curved spacetime
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abstract
It is an article of folklore that the collection of ideas identified as Euclidean quantum gravity may be derived from ordinary Lorentzian signature gravity by the procedure of Wick rotation. This note will attempt to shed some light on this relatively ill-understood procedure. I argue that it proves inappropriate and unhelpful to regard Wick rotation in terms of a complex deformation of the time coordinate. Rather, Wick rotation can more usefully be viewed as a complex deformation of the spacetime metric. This simple reformulation of the Wick rotation procedure, while it leaves flat space physics unaffected, has profound implications for quantum gravity.
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Without Lorentz invariance, double Wick rotations connect inequivalent field theories in flat spacetime, with criteria for when propagating modes, unitarity, and renormalizability fail to translate.
Review of spectral noncommutative geometry applied to the Standard Model, including bosonic and fermionic actions, Euclidean vs Lorentz issues, and going beyond the SM.
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Spectral Noncommutative Geometry, Standard Model and all that
Review of spectral noncommutative geometry applied to the Standard Model, including bosonic and fermionic actions, Euclidean vs Lorentz issues, and going beyond the SM.