Gauge symmetries in spin-foam gravity: the case for "cellular quantization"

Area of Science:

• Theoretical Physics
• Quantum Gravity
• Mathematical Physics

Background:

• The spin-foam approach is a method for quantizing gravity.
• BF theory is a key component in this approach, utilizing 2-complexes and group representations.
• Existing spin-foam quantization methods face challenges with gauge symmetries in higher dimensions.

Purpose of the Study:

• To identify inconsistencies in the spin-foam quantization of BF theory in three dimensions and higher.
• To propose and describe a generalized quantization method consistent with discrete BF theory's gauge symmetries.
• To clarify the foundational aspects and limitations of the spin-foam formalism.

Main Methods:

• Analysis of the spin-foam quantization of BF theory in the context of 2-complexes and group representations.
• Identification of necessary amendments for consistency with gauge symmetries in discrete BF theory.
• Development and discussion of a generalized
• cellular quantization
• framework.

Main Results:

• Spin-foam quantization requires amendments in dimensions three and higher to ensure consistency with discrete BF theory's gauge symmetries.
• The proposed
• cellular quantization
• is finite and generates a topological invariant.
• This new method aligns with the properties of continuum BF theory and its loop quantization.

Conclusions:

• The study clarifies the foundations and limitations of the spin-foam approach to quantum gravity.
• Cellular quantization provides a consistent discrete framework for BF theory.
• This work paves the way for understanding symmetry-breaking in discrete quantum gravity.