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Quantum fields without Wick rotation
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We discuss the calculation of one-loop effective actions in Lorentzian spacetimes, based on a very simple application of the method of steepest descent to the integral over the field. We show that for static spacetimes this procedure agrees with the analytic continuation of Euclidean calculations. We also discuss how to calculate the effective action by integrating a renormalization group equation. We show that the result is independent of arbitrary choices in the definition of the coarse-graining and we see again that the Lorentzian and Euclidean calculations agree. When applied to quantum gravity on static backgrounds, our procedure is equivalent to analytically continuing time and the integral over the conformal factor.
Forward citations
Cited by 3 Pith papers
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Self-consistent graviton spectral function in Lorentzian quantum gravity
A self-consistent spectral renormalisation group computation yields a positive, normalizable graviton spectral function with a massless pole and a multi-graviton continuum decaying as 1/(λ² log³ λ²).
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Matter Spectral Functions from Quantum Gravity
Under asymptotically safe quantum gravity, photon and scalar propagators acquire Källén-Lehmann spectral functions that are non-normalizable and change sign in the ultraviolet.
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Wick-connected theories and Lorentz violation
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.
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