Cancellation of ultra-violet infinities in one loop gravity

TL;DR

This paper recounts the historical discovery in 1974 that ultra-violet divergences cancel in one-loop quantum gravity without matter, a significant step in understanding quantum gravitational effects.

Contribution

It presents the original discovery of divergence cancellation in one-loop quantum gravity, a foundational result in the field.

Findings

Ultra-violet divergences cancel on mass shell in one-loop quantum gravity.

The work was independently discovered alongside t'Hooft and Veltman.

This note provides historical context and original insights into the cancellation phenomenon.

Abstract

This is a historical note. In 1974 I was an undergraduate student of L.D. Faddeev. I was working on quantum gravity [without matter] in one loop approximation. I discovered [simultaneously with G. t'Hooft M. Veltman] that on mass shell ultra-violet divergences cancel. The submission is a translation of the Diploma.