Mathematics plays a crucial role in the study of representation theory and its applications in quantum mechanics. Representation theory provides a framework for understanding symmetries in quantum systems, which are essential in describing physical phenomena. By using mathematical concepts such as group theory and linear algebra, representation theory helps physicists analyze the behavior of quantum systems and make predictions about their properties. In quantum mechanics, representations of symmetry groups help classify particles and understand the interactions between them. Overall, mathematics is the language that allows physicists to formalize and study the intricate relationships between symmetries, quantum states, and physical observables in quantum mechanics.
