Harish-Chandra integral

The Harish-Chandra integral is a concept from integral calculus that originated in the study of harmonic analysis on Lie groups. Closely related is the Harish-Chandra formula which is used to evaluate the integral.

The integrals are named after the Indian mathematician Harish-Chandra, who proved in 1957 the so-called Harish-Chandra formula. Today, the integral and its associated formula find applications in many fields, such as representation theory, random matrix theory and quantum field theory.

A special case is the formula for integrals over the unitary group which was independently discovered in 1980 by Claude Itzykson and Jean-Bernard Zuber and applied to quantum field theory. The integral over the unitary group is also referred to as the Harish-Chandra–Itzykson–Zuber integral.

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