Study on Berry phase, fractional charge and chiral anomaly

• Main Authors: Ming-Chiun Wu, 吳銘群
• Other Authors: Yeong-Chuan Kao
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/93948016126596501629

博士 === 國立臺灣大學 === 物理研究所 === 100 === We study the connection between Berry phase, fractional charge and Chiral anomaly. Their close relationship can be most easily seen through the Goldstone-Wilczek model, whose vacuum has been known to acquire non-trivial fractional charge due to the coupling of the fermion field to a topological nontrivial soliton field, and at zero temperature this charge fractionalization has been argued to be related to both the phase-space Berry phase and chiral anomaly. However, Fujikawa recently shows that there are some basic differences between Berry phase and chiral anomaly. It suggests that the mix of the concept of fractional charge, Berry phase and Chiral anomaly together might be problematic. In this article we will try to clarify this point. To achieve this goal, we find that it is useful to study this system at finite temperature. Here we first study this problem in a framework in which the connection of charge fractionalization to the chiral anomaly is manifest. In this formalism, the fermion number can be found to be separated into two terms: one is related to chiral anomaly which is temperature independent, and the other is the temperature correction term. As a result, it becomes manifest why while fractional charge is temperature dependent but chiral anomaly is temperature independent. Moreover, the temperature correction term can be seen to be simply the massive Schwinger model. The temperature dependence of the induced charge is then solved by doing the one loop calculation of the massive Schwinger model, and is found, in consistent with the previous studies, to decrease as temperature arises and vanish at infinite temperature. Then, as a direct generalization, we restudy the induced Chern-Simons term at finite temperature. We find that, for spatially uniform but time dependent background gauge fields, the effective action is also separated into two parts: one is the chiral Jacobian which is temperature independent, and the other is related to an effective massive Schwinger model which gives the temperature correction. By explicitly calculating the one loop result of the massive Schwinger model part, we find that the well known temperature correction to the induced Chern-Simons term can be reproduced. The above two parts are based on the paper which has been accepted and will be published in Physical Review D. Finally, to see the connection of fractional charge and Berry phase, we adopt Fujikawa’s second quantization method. By explicitly studying the temperature effect on Berry phase, it is also found that the fractional charge is different to this Berry phase at finite temperature.