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Advances in Mathematical Physics
Volume 2010, Article ID 191529, 16 pages
Review Article

New Affine Coherent States Based on Elements of Nonrenormalizable Scalar Field Models

1Department of Physics, University of Florida, Gainesville, FL 32611, USA
2Department of Mathematics, University of Florida, Gainesville, FL 32611, USA

Received 23 December 2009; Accepted 15 April 2010

Academic Editor: S. T. Ali

Copyright © 2010 John R. Klauder. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Recent proposals for a nontrivial quantization of covariant, nonrenormalizable, self-interacting, scalar quantum fields have emphasized the importance of quantum fields that obey affine commutation relations rather than canonical commutation relations. When formulated on a spacetime lattice, such models have a lattice version of the associated ground state, and this vector is used as the fiducial vector for the definition of the associated affine coherent states, thus ensuring that in the continuum limit, the affine field operators are compatible with the system Hamiltonian. In this article, we define and analyze the associated affine coherent states as well as briefly review the author's approach to nontrivial formulations of such nonrenormalizable models.