Correlation functions for multi-matrix models and quaternion determinants |
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| Institution: | 1. School of Information Science and Technology, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;2. Australian National University, Canberra, ACT 2600, Australian;1. School of Mathematical Sciences, Peking University, Beijing, 100871, China;2. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China;1. School of Computer Science and Technology, Huazhong University of Science and Technology, China;2. School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, China;1. School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou 221116, China;2. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China;1. Department of Mathematics, China University of Mining and Technology, Beijing 100083, China;2. Department of Mathematics and Statistics, ARC centre of excellence for mathematical and statistical frontiers, the University of Melbourne, Victoria 3010, Australia |
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| Abstract: | Using a close relationship to the Brownian motion model of random matrices, multi-matrix models in quantum field theory are analyzed. In the case many hermitian matrices are connected in a chain and one of them has a restricted (real symmetric, self dual real quaternion or antisymmetric hermitian) symmetry, the multi-matrix multi-level correlation functions are shown to have quaternion determinant forms. |
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