Vacuum Nodes and Anomalies in Quantum Theories
Abstract
We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple geometric terms. We analyse in detail two different archetypical systems: i) the planar rotor with a nontrivial magnetic flux Φ and ii) the Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any reflection invariant potential V is encoded in the nodal structure of the unique vacuum for θ=π. In the second case we prove that the nodes of the first Landau level for unit magnetic charge appear at the crossing of the two noncontractible circles α_{}, β_{} with holonomies h_{α}(A)=h_{β}(A)=1 for any reflection invariant potential V. This property illustrates the geometric origin of the quantum translation anomaly.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2001
 DOI:
 10.1007/s002200100390
 arXiv:
 arXiv:hepth/0010227
 Bibcode:
 2001CMaPh.218..233A
 Keywords:

 High Energy Physics  Theory
 EPrint:
 14 pages, 2 psfigures, to appear in Commun. Math. Phys