2 research outputs found
Quantum geometry with intrinsic local causality
The space of states and operators for a large class of background independent
theories of quantum spacetime dynamics is defined. The SU(2) spin networks of
quantum general relativity are replaced by labelled compact two-dimensional
surfaces. The space of states of the theory is the direct sum of the spaces of
invariant tensors of a quantum group G_q over all compact (finite genus)
oriented 2-surfaces. The dynamics is background independent and locally causal.
The dynamics constructs histories with discrete features of spacetime geometry
such as causal structure and multifingered time. For SU(2) the theory satisfies
the Bekenstein bound and the holographic hypothesis is recast in this
formalism.Comment: Latex 33 pages, 7 Figure, epsfi
A candidate for a background independent formulation of M theory
A class of background independent membrane field theories are studied, and
several properties are discovered which suggest that they may play a role in a
background independent form of M theory. The bulk kinematics of these theories
are described in terms of the conformal blocks of an algebra G on all oriented,
finite genus, two-surfaces. The bulk dynamics is described in terms of causal
histories in which time evolution is specified by giving amplitudes to certain
local changes of the states. Holographic observables are defined which live in
finite dimensional states spaces associated with boundaries in spacetime. We
show here that the natural observables in these boundary state spaces are, when
G is chosen to be Spin(D) or a supersymmetric extension of it, generalizations
of matrix model coordinates in D dimensions. In certain cases the bulk dynamics
can be chosen so the matrix model dynamics is recoverd for the boundary
observables. The bosonic and supersymmetric cases in D=3 and D=9 are studied,
and it is shown that the latter is, in a certain limit, related to the matrix
model formulation of M theory. This correspondence gives rise to a conjecture
concerning a background independent form of M theory in terms of which
excitations of the background independent membrane field theory that correspond
to strings and D0 branes are identified.Comment: Latex 46 pages, 21 figures, new results included which lead to a
modification of the statement of the basic conjecture. Presentation improve