An Itzykson-Zuber-like Integral and Diffusion for Complex Ordinary and Supermatrices
Thomas Guhr, Tilo Wettig
TL;DR
This paper extends the Itzykson-Zuber integral to arbitrary complex matrices, including supermatrices, using a diffusion equation approach, with implications for quantum field theories.
Contribution
It introduces a novel integral for complex matrices and adapts the diffusion method to supermatrices, broadening the mathematical tools for quantum physics applications.
Findings
Derived an analogue of the Itzykson-Zuber integral for complex matrices
Extended the diffusion equation method to supermatrix spaces
Potential applications in Quantum Chromodynamics and Quantum Gravity
Abstract
We compute an analogue of the Itzykson-Zuber integral for the case of arbitrary complex matrices. The calculation is done for both ordinary and supermatrices by transferring the Itzykson-Zuber diffusion equation method to the space of arbitrary complex matrices. The integral is of interest for applications in Quantum Chromodynamics and the theory of two-dimensional Quantum Gravity.
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