1201.6505 (C. Wetterich)

Geometry and symmetries in lattice spinor gravity    [PDF]

C. Wetterich

Lattice spinor gravity is a proposal for regularized quantum gravity based on
fermionic degrees of freedom. In our lattice model the local Lorentz symmetry
is generalized to complex transformation parameters. The difference between
space and time is not put in a priori, and the euclidean and Minkowski quantum
field theory are unified in one functional integral. The metric and its
signature arise as a result of the dynamics, corresponding to a given ground
state or cosmological solution. Geometrical objects as the vierbein, spin
connection or the metric are expectation values of collective fields built from
an even number of fermions. The quantum effective action for the metric is
invariant under general coordinate transformations in the continuum limit. The
action of our model is found to be also invariant under gauge transformations.
We observe a "geometrical entanglement" of gauge- and Lorentz-transformations
due to geometrical objects transforming non-trivially under both types of
symmetry transformations.

View original: http://arxiv.org/abs/1201.6505