Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998tx19.confe.135w&link_type=abstract
Abstracts of the 19th Texas Symposium on Relativistic Astrophysics and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.:
Astronomy and Astrophysics
Astrophysics
Scientific paper
Current efforts to form a quantum theory of gravity are hampered by not having a ``picture'' that tells us what to expect. We obtain such a picture by demanding scale invariance of a spacetime containing fields of various conformal weights. The presence of the fields requires grading of the conformal gauge theory, leading to graded conformal gauge theories (GCGTs). Each GCGT is the local direct product of the phase space of a Weyl geometry with the integers. Conformally self-dual scalar fields on this structure form a Hilbert space, so the class of geometries is large enough to describe both gravity and quantum structures. GCGTs have many other properties of quantum systems, including an almost complex structure, canonical commutators of phase space variables and geodesics obeying a Schrodinger equation. These properties require no assumptions beyond the original scale invariance.
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