Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.physletb.2005.03.063
Title: Sigma model Lagrangian for the Heisenberg group
Authors: Baaquie, B.E. 
Kok, K.Y.
Keywords: Chiral symmetry
Cubic Lagrangian
Duality transformation
Heisenberg Lagrangian
Sigma models
Issue Date: 26-May-2005
Citation: Baaquie, B.E., Kok, K.Y. (2005-05-26). Sigma model Lagrangian for the Heisenberg group. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 615 (1-2) : 134-140. ScholarBank@NUS Repository. https://doi.org/10.1016/j.physletb.2005.03.063
Abstract: We study the Lagrangian for a sigma model based on the non-compact Heisenberg group. A unique feature of this model - unlike the case for compact Lie groups - is that the Lagrangian has to be regulated since the trace over the Heisenberg group is otherwise divergent. The resulting theory is a real Lagrangian with a quartic interaction term. In particular, in D=2 space-time dimensions, after a few non-trivial transformations, the Lagrangian is shown to be equivalent, at the classical level, to a complex cubic Lagrangian. A one-loop computation confirms that the quartic and cubic Lagrangians are equivalent at the quantum level as well. The complex Lagrangian is known to be classically equivalent to the SU(2) sigma model, with the equivalence breaking down at the quantum level. An explanation of this well-known results emerges from the properties of the Heisenberg sigma model. © 2005 Elsevier B.V. All rights reserved.
Source Title: Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/97917
ISSN: 03702693
DOI: 10.1016/j.physletb.2005.03.063
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