Adroja, PavanPavanAdrojaAmrutiya, SanjaySanjayAmrutiyaPatil, RiddhiRiddhiPatil2026-03-062026-03-062026-02-0110.48550/arXiv.2602.18781https://repository.iitgn.ac.in/handle/IITG2025/34775We develop a theory of smooth relative connections over the real path algebra ?Q on smooth twisted quiver bundles. We give obstructions to the existence of a smooth relative connection on twisted quiver bundles. For tree-type quiver bundles, we establish a necessary and sufficient condition for the existence of a smooth relative connection. Additionally, we provide a framework for the representation theory of flat quiver bundles, relating the existence of flat relative connections to the underlying quiver representations.en-USe-Print