Speaker
Description
We address the problem of the SU(2) internal symmetry in Loop Quantum Cosmology (LQC) and its relationship with canonical Loop Quantum Gravity (LQG). We introduce new tools to treat non-diagonal Bianchi models in LQC, and we discuss the Gauss constraint and the role of gauge freedom. This allows us to prove that, in the minisuperspace cosmological framework, there exist suitable variables in which the Gauss constraint can be recast into three Abelian constraints.
We identify the Gauss constraint as the primary element that connects the SU(2) group with the full quantum theory (LQG). Building on these new results, we seek an approach to the cosmological sector that preserves the Gauss constraint, requiring to move beyond the minisuperspace framework. We propose a strategy to face this challenge, based on the geometric structure underlying Yang-Mills theories.
