Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-11-14
Phys.Rev. D73 (2006) 025017
Physics
High Energy Physics
High Energy Physics - Theory
28 pages. The last sentence in Abstract has been changed, the last paragraph in Section 1 has been re-written, and the latter
Scientific paper
10.1103/PhysRevD.73.025017
It is sometimes stated in the literature that the quantum anomaly is regarded as an example of the geometric phase. Though there is some superficial similarity between these two notions, we here show that the differences bewteen these two notions are more profound and fundamental. As an explicit example, we analyze in detail a quantum mechanical model proposed by M. Stone, which is supposed to show the above connection. We show that the geometric term in the model, which is topologically trivial for any finite time interval $T$, corresponds to the so-called ``normal naive term'' in field theory and has nothing to do with the anomaly-induced Wess-Zumino term. In the fundamental level, the difference between the two notions is stated as follows: The topology of gauge fields leads to level crossing in the fermionic sector in the case of chiral anomaly and the {\em failure} of the adiabatic approximation is essential in the analysis, whereas the (potential) level crossing in the matter sector leads to the topology of the Berry phase only when the precise adiabatic approximation holds.
No associations
LandOfFree
Quantum anomaly and geometric phase; their basic differences does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum anomaly and geometric phase; their basic differences, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum anomaly and geometric phase; their basic differences will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-218724