ANOMALIES AT FINITE TEMPERATURE AND DENSITY

Abstract

Chiral anomalies for Abelian and non-Abelian quantum field theories at finite temperature and density (FTFD) are analyzed in detail in both imaginary and real time (IT and RT) formalisms. IT and RT triangle diagrams and IT functional methods (à la Fujikawa) are used at FTFD. The vector anomaly (the one regarding the lepton and baryon numbers) in the Weinberg–Salam theory, for an arbitrary number of fermion families, is also treated using IT functional methods at FTFD. In all cases, the expressions for the FTFD anomalies (as functions of the corresponding quantities) turn out to be identical to those at zero temperature and density, thereby extending previous results by various authors for the finite temperature and zero density case. Moreover, the independence of anomalies from temperature and density is shown to be consistent, at least in the Abelian case, with the analytic continuation from the IT formulation to the RT one.