Quantum fields without Wick rotation

Understand

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.