1110.1539 (C. Wetterich)

Lattice diffeomorphism invariance    [PDF]

C. Wetterich

We propose a lattice counterpart of diffeomorphism symmetry in the continuum.
A functional integral for quantum gravity is regularized on a discrete set of
space-time points, with fermionic or bosonic lattice fields. When the
space-time points are positioned as discrete points of a continuous manifold,
the lattice action can be reformulated in terms of average fields within local
cells and lattice derivatives. Lattice diffeomorphism invariance is realized if
the action is independent of the positioning of the space-time points. Regular
as well as rather irregular lattices are then described by the same action.
Lattice diffeomorphism invariance implies that the continuum limit and the
quantum effective action are invariant under general coordinate transformations
- the basic ingredient for general relativity. In our approach the lattice
diffeomorphism invariant actions are formulated without introducing a metric or
other geometrical objects as fundamental degrees of freedom. The metric rather
arises as the expectation value of a suitable collective field. As examples, we
present lattice diffeomorphism invariant actions for a bosonic non-linear
sigma-model and lattice spinor gravity.

View original: http://arxiv.org/abs/1110.1539