2 research outputs found
Quantum Geons and Noncommutative Spacetimes
Physical considerations strongly indicate that spacetime at Planck scales is
noncommutative. A popular model for such a spacetime is the Moyal plane. The
Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the
latter is not appropriate for more complicated spacetimes such as those
containing the Friedman-Sorkin (topological) geons. They have rich
diffeomorphism groups and in particular mapping class groups, so that the
statistics groups for N identical geons is strikingly different from the
permutation group . We generalise the Drinfel'd twist to (essentially)
generic groups including to finite and discrete ones and use it to modify the
commutative spacetime algebras of geons as well to noncommutative algebras. The
latter support twisted actions of diffeos of geon spacetimes and associated
twisted statistics. The notion of covariant fields for geons is formulated and
their twisted versions are constructed from their untwisted versions.
Non-associative spacetime algebras arise naturally in our analysis. Physical
consequences, such as the violation of Pauli principle, seem to be the outcomes
of such nonassociativity.
The richness of the statistics groups of identical geons comes from the
nontrivial fundamental groups of their spatial slices. As discussed long ago,
extended objects like rings and D-branes also have similar rich fundamental
groups. This work is recalled and its relevance to the present quantum geon
context is pointed out.Comment: 41 page