An $O(3)$ Global Anomaly in 0+1 Dimension

Details An $O(3)$ Global Anomaly in 0+1 Dimension An $O(3)$ Global Anomaly in 0+1 Dimension

1993-09-17

arxiv.org/abs/hep-ph/9309278v1

Mod.Phys.Lett. A9 (1994) 623-626

Physics

High Energy Physics

High Energy Physics - Phenomenology

7 pages+3 figures available upon request, NBI-HE-93-53

Scientific paper

10.1142/S0217732394003853

We present a simple exactly solvable quantum mechanical example of the global anomaly in an $O(3)$ model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, $\pi_1 (O(3)) ={\bf Z}_2$, fermionic level crossing or circling occur in the eigenvalue spectrum of the 1-dim. Dirac \op under continuous external field transformations. They are shown to be related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate 2-dim. Dirac \op . We argue that fermionic degrees of freedom in the presence of an infinitely large external field violate perturbative decoupling.

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