index theorems

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Theories in mathematics that relate the solutions of an equation to topology associated with the equation. There are many applications of index theorems to gauge theories, quantum gravity, supersymmetry, string theory, and certain problems in the theory of condensed matter. Examples of index theorems in the case of gauge fields coupled to fermion fields (of the type relevant to the description of elementary particles) are that solutions of the Dirac equation are related to topological invariants of gauge theories. This application of index theorems is closely related to chiral anomalies. Index theorems also give the number of parameters associated with instantons and magnetic monopoles.

Subjects: Physics.

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