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**UNC-CH Physics and Astronomy Colloquium**

Steven Christensen, University of North Carolina at Chapel Hill

**“The Schwinger-DeWitt Proper Time Algorithm: A History”**

Much of my career in physics has been, in one way or another, concerned with the use of the so-called Schwinger-DeWitt proper time algorithm for studying renormalization in quantum field theory in curved spacetimes. As a student of Bryce DeWitt, at UNC-CH and at UT- Austin, I was introduced to Schwingerâ€™s classic 1951 paper, On Gauge Invariance and Vacuum Polarization, Phys. Rev. 82, Vol. 5, pages 664-679. I became aware of DeWitt’s curved space generalizations of the algorithm through detailed chapters in his book Dynamical Theory of Groups and Fields, Gordon and Breach, 1965, based on his 1963 Les Houches lectures. Since then, I, and many others, have used this technique and extensions of it to understand things like black hole radiation and back reaction, trace and other anomalies, index theorems, and more. In this talk I will present a short history of how the method has been the motivation for developments in physics, mathematics, and even computer software.