Itzykson-Zuber Integral

The Itzykson-Zuber integral is a mathematical tool used in quantum physics and random matrix theory to compute averages involving large, complex matrices. It simplifies the integration over the space of unitary matrices—those preserving length—by expressing these integrals in terms of the matrices' eigenvalues (their characteristic values). Essentially, it transforms a complicated integral over all possible orientations into a manageable formula based on eigenvalues, facilitating calculations in theoretical physics and related fields dealing with systems characterized by symmetry and complex interactions.