On Measurement and Invariant Structure in Quantum Mechanics

This paper examines measurement and representational limits within a geometric formulation of quantum mechanics based on connection geometry and holonomy. Measurement is interpreted as projection onto invariant quantities associated with comparison of states under parallel transport. This projection preserves invariant phase relations while discarding non-invariant information. As a result, measurement outcomes appear discrete and probabilistic at the representational level. Correlations between subsystems arise from shared geometric structure and exhibit nonlocal consistency without introducing additional dynamical mechanisms. The analysis clarifies how measurement and classical behavior can be understood within a geometric account of quantum kinematics.