An O(3) global anomaly in \(0+1\) dimension

DOI10.1142/S0217732394003853zbMATH Open1021.81906arXivhep-ph/9309278OpenAlexW3098385529MaRDI QIDQ2727967

Minos Axenides, Andrei Johansen, Holger Bech Nielsen

Publication date: 31 July 2001

Published in: Modern Physics Letters A (Search for Journal in Brave)

Abstract: 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, $$, 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.

Full work available at URL: https://arxiv.org/abs/hep-ph/9309278

Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) Anomalies in quantum field theory (81T50) General mathematical topics and methods in quantum theory (81Q99)

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