Exact Results in Quantum Theory

A great deal of interest has recently arisen in high-precision atomic physics studies, which are aimed at searching for New Physics beyond the Standard Model (SM). These studies have become possible thanks to advances in the experimental quantum control of matter and light, as well as in many-body relativistic methods. In the present talk, we will look at one example of the research devoted to the quest for a hypothetical fifth force, based on the analysis of isotope shifts in ions. We will demonstrate that an accurate theoretical account of higher-order SM contributions is essential to understanding the available experimental findings.