Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case

Details Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case

2009-05-20

arxiv.org/abs/0905.3253v2

J. Phys. A: Math. Theor. 42, 275205, (2009)

Physics

Mathematical Physics

37 pages

Scientific paper

10.1088/1751-8113/42/27/275205

Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary orthogonally and unitary-symplectically invariant matrix ensembles. The results are equivalent to, but the approach is different from the superbosonization formula. We express our results in a unifying way. We also give explicit expressions for all one-point functions and discuss features of the higher order correlations.

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