The utility of coherent states and other mathematical methods in the foundations of affine quantum gravity
Abstract
Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity, (ii) a regularized projection operator procedure to accomodate first and secondclass quantum constraints, and (iii) a hardcore interpretation of nonlinear interactions to understand and potentially overcome nonrenormalizability. In this program, some of the less traditional mathematical methods employed are (i) coherent state representations, (ii) reproducing kernel Hilbert spaces, and (iii) functional integral representations involving a continuoustime regularization. Of special importance is the profoundly different integration measure used for the Lagrange multiplier (shift and lapse) functions. These various concepts are first introduced on elementary systems to help motivate their application to affine quantum gravity.
 Publication:

Physics of Atomic Nuclei
 Pub Date:
 October 2005
 DOI:
 10.1134/1.2121924
 arXiv:
 arXiv:hepth/0401214
 Bibcode:
 2005PAN....68.1739K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 15 pages, Presented at the XInternational Conference on Symmetry Methods in Physics