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The diagonalization of Hermitian supermatrices is studied. Such a change ofcoordinates is inevitable to find certain structures in random matrix theory.However it still poses serious problems since up to now the calculation of allRothstein contributions known as Efetov-Wegner terms in physics was quitecumbersome. We derive the supermatrix Bessel function with all Efetov-Wegnerterms for an arbitrary rotation invariant probability density function. Asapplications we consider representations of generating functions for Hermitianrandom matrices with and without an external field as integrals overeigenvalues of Hermitian supermatrices. All results are obtained with allEfetov-Wegner terms which were unknown before in such an explicit and compactrepresentation.

On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix