The utility of coherent states and other mathematical methods in the foundations of affine quantum gravity

Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity (ii) a regularized projection operator procedure to accommodate first- and second-class quantum constraints, and (iii) a hard-core interpretation of nonlinear interactions to understand and potentially overc...

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Bibliographic Details
Published in:Physics of atomic nuclei 2005-10, Vol.68 (10), p.1739-1745
Main Author: Klauder, J. R.
Format: Article
Language:English
Subjects:
ANNIHILATION OPERATORS
COMMUTATION RELATIONS
EIGENSTATES
HILBERT SPACE
KERNELS
NONLINEAR PROBLEMS
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
PROJECTION OPERATORS
QUANTUM GRAVITY
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Summary:Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity (ii) a regularized projection operator procedure to accommodate first- and second-class quantum constraints, and (iii) a hard-core 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 continuous-time 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.
ISSN:1063-7788
1562-692X
DOI:10.1134/1.2121924