Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-01-27
Phys.Atom.Nucl. 68 (2005) 1739-1745; Yad.Fiz. 68 (2005) 1801-1807
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, Presented at the X-International Conference on Symmetry Methods in Physics
Scientific paper
10.1134/1.2121924
Affine quantum gravity involves (i) affine commutation relations to ensure metric positivity, (ii) a regularized projection operator procedure to accomodate 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.
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