Anomaly on quantum gases in one and two dimensions*

Nonrelativistic quantum scale anomalies have recently received some attention in the AMO community, especially in the context of cold atoms. Based on previous formal work by H. Camblong (USF) and C. Ordonez, in 2015 it was proposed a systematic study of anomalous effects in such systems using path integrals, with the initial emphasis on the thermodynamics of 2D systems.  After several formal studies, a recently developed framework for the understanding of the virial expansion in homogeneous 2D gases (Fermions in particular). This framework helped us develop a description of anomalies in 1D, 3-body Fermionic systems.  The purpose of this talk is to give a review of the conceptual background and philosophy of our approach and of recent results, as well as of current and future collaborations and projects.