Note on anomalies in field theories

摘要: In this note, we investigate the anomalies in field theories. The results of the anomalies through Feynman diagrams calculation are multi-valued function. These single-valued branches of multi-valued function are related to the bound states of neutral pseudoscalar mesons. Adding these bound state contributions, we obtain a new anomaly free condition that all the external particles are on-shell and find the non-perturbative mass spectrum of neutral pseudoscalar mesons. We also discuss the anomaly in 2 dimensional QFT.