Quantum Anomalies, Path Integrals and Quantum Field Theory Virial Theorems for Cold Atoms and Similar Systems
Abstract
It has been known for some time that systems with contact interactions may develop quantum anomalies, i.e., that their classical SO(2,1) conformal symmetries may not survive the quantization process. -trapped cold-atom systems, while their action doesn’t exhibit this symmetry, still realize a “hidden” SO(2,1) algebra classically. When quantized, the anomalies may spoil the symmetry and this algebra becomes “open”, the “extra term” being essentially what is known in the AMO literature as the (Tan) “contact” term. There has recently been a great of deal of interest in measuring these anomaly effects in such systems, and different authors have performed the relevant calculations. However, some of the zero-temperature anomaly predictions seem to be in contradiction with experimental findings at slightly finite temperatures. As pointed out in a recent review, a deeper understanding of conceptual and technical issues concerning anomalies, the interplay between zero and finite-temperature and other effects (explicit symmetry breaking, e.g., due to a small third dimension) is mandatory, and a systematic and comprehensive treatment and comparison between the different methods used is in order before definitive answers extracted from the experiments are given. The PI is an expert on the mathematical aspects of quantum anomalies for systems and is proposing to do this comprehensive study for such systems, with the novel use in this field of Fujikawa’s path-‐ integral methods.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 11, 2016
- Source ID
- W911NF1510445
Entities
People
- Carlos Ordonez
Organizations
- Army Contracting Command
- Office of the Secretary of Defense
- Texas A&M University–Victoria