Gauge symmetries in spinfoam gravity: the case for "cellular quantization"

TL;DR

This paper proposes a refined 'cellular quantization' method for spinfoam quantum gravity that preserves gauge symmetries, ensuring finiteness and topological invariance, thus clarifying foundational aspects of the formalism.

Contribution

It introduces 'cellular quantization' as a consistent extension of spinfoam quantization that aligns with continuum BF theory and its loop quantization, addressing key limitations.

Findings

Cellular quantization is finite and topologically invariant.

It matches properties of continuum BF theory.

It clarifies the role of gauge symmetries in discrete quantum gravity.

Abstract

The spinfoam approach to quantum gravity rests on a "quantization" of BF theory using 2-complexes and group representations. We explain why, in dimension three and higher, this "spinfoam quantization" must be amended to be made consistent with the gauge symmetries of discrete BF theory. We discuss a suitable generalization, called "cellular quantization", which (1) is finite, (2) produces a topological invariant, (3) matches with the properties of the continuum BF theory, (4) corresponds to its loop quantization. These results significantly clarify the foundations - and limitations - of the spinfoam formalism, and open the path to understanding, in a discrete setting, the symmetry-breaking which reduces BF theory to gravity.