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Group theory is a mathematical framework that describes the symmetries of an object or a system. A group is a set of elements with a binary operation (such as multiplication or addition) that satisfies certain properties, including closure, associativity, identity, and invertibility. Group theory provides a powerful tool for analyzing the symmetries of a system and predicting its behavior.
The representation theory of groups is a powerful tool for analyzing the symmetries of physical systems. In essence, a representation of a group is a way of associating matrices or linear transformations with the elements of the group.
Group theory is used to study the symmetries of crystals and other condensed matter systems. This helps physicists understand the behavior of materials and predict their properties.
Symmetry in QM, basic group definitions, subgroups, and classes. Representations
