The discussion centers on the action of the isospin operator I_3 on the state |ud>, which represents a combination of up and down quarks. Participants clarify that the focus is on whether |ud> is an eigenstate of the isospin operator I_3. The consensus is that |ud> is not an eigenstate of I_3, as it is a superposition of different isospin states. The conversation emphasizes the importance of understanding isospin in particle physics and its implications for quark states. Overall, the thread highlights the nuances of isospin operators in quantum mechanics.