Mathematics
Scientific paper
Feb 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982natur.295..667p&link_type=abstract
Nature, vol. 295, Feb. 25, 1982, p. 667, 678.
Mathematics
5
Conformal Mapping, Cosmology, Gravitation Theory, Quantum Theory, Singularity (Mathematics), Space-Time Functions, Cosmic Dust, Degrees Of Freedom, Energy Distribution, Green'S Functions, Wave Functions
Scientific paper
A simplified quantum model of gravity is presented with quantization of the conformal degree of freedom only as an examination of the persistence of singularities in the quantum domain. Quantum conformal fluctuations were observed to diverge at the classical singularity in the study of dust particles. A wavefunction propagating with a kernel was formulated to account for the lack of space-time geometry in the quantum regime, and given a physical interpretation by inclusion of a Gaussian wavepacket for the kernel, which dispersed as the final hypersurface approached the singularity. The divergence of the retarded Green's function was assumed, then deduced from the conformal invariance of the scalar wave operator. The behavior of the Green's function as a second hypersurface (expressed as time) approaches zero was explored, and found to approach infinity, implying the conclusion is true for general distributions of matter and energy.
Narlikar Jayant V.
Padmanabhan Thanu
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