Chiral anomaly of massless fermion at finite temperature and chemical potential

摘要

In this paper, using the imaginary-time temperature field theory, we discuss the possible modification of chiral anomaly of a massless fermion in (3+1)-dimensional QED (QED4) when the temperature and chemical potential effects are included. It is found that the chiral anomaly is independent of the temperature and chemical potential. Meanwhile, we also introduce the chemical potential corresponding to chiral charge, and find that it will induce a Chern-Simons-like term, which has similar C transformation properties (and opposite P transformation property) to the corresponding Chern-Simons term in (2+1)-dimensional QED (QED_3). More importantly, we find that when the chemical potential corresponding to the fermion number is space-dependent, it will induce an extra anomaly term. It is expected that this can yield new physical effects.