Quantum Scars in Quantum Field Theory

We develop the theory of quantum scars for quantum ﬁelds. By generalizing the formalisms of Heller and Bogomolny from few-body quantum mechanics to quantum ﬁelds, we ﬁnd that unstable periodic classical solutions of the ﬁeld equations imprint themselves in a precise manner on bands of energy eigenfunctions. This indicates a breakdown of thermalization at certain energy scales, in a manner that can be characterized via semiclassics. As an explicit example, we consider time-periodic non-topological solitons in complex scalar ﬁeld theories. We ﬁnd that an unstable variant of Q-balls, called Q-clouds, induce quantum scars. Some technical contributions of our work include methods for characterizing moduli spaces of periodic orbits in ﬁeld theories, which are essential for formulating our quantum scar formula. We further discuss potential connections with quantum many-body scars in Rydberg atom arrays.