2019年7月1日
A random matrix model with non-pairwise contracted indices
Progress of Theoretical and Experimental Physics
- ,
- 巻
- 2019
- 号
- 7
- 開始ページ
- 073A01
- 終了ページ
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1093/ptep/ptz057
- 出版者・発行元
- Oxford University Press (OUP)
<title>Abstract</title>
We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the $p$-spin spherical model for the spin glass. We analyze the model using Feynman diagrammatic expansions, and provide an exhaustive characterization of the graphs that dominate when the dimensions of the pairwise and (or) non-pairwise contracted indices are large. We apply this to investigate the properties of the wave function of a toy model closely related to a tensor model in the Hamilton formalism, which is studied in a quantum gravity context, and obtain a result in favor of the consistency of the quantum probabilistic interpretation of this tensor model.
We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the $p$-spin spherical model for the spin glass. We analyze the model using Feynman diagrammatic expansions, and provide an exhaustive characterization of the graphs that dominate when the dimensions of the pairwise and (or) non-pairwise contracted indices are large. We apply this to investigate the properties of the wave function of a toy model closely related to a tensor model in the Hamilton formalism, which is studied in a quantum gravity context, and obtain a result in favor of the consistency of the quantum probabilistic interpretation of this tensor model.
- リンク情報
-
- DOI
- https://doi.org/10.1093/ptep/ptz057
- arXiv
- http://arxiv.org/abs/arXiv:1903.05944
- 共同研究・競争的資金等の研究課題
- データ解析の数学的手法が描く正準テンソル模型の時空描像と時空概念の普遍性
- 共同研究・競争的資金等の研究課題
- 正準テンソル模型がつなぐ量子重力とランダムテンソルネットワーク
- 共同研究・競争的資金等の研究課題
- テンソル模型による量子重力へのアプローチ及び強く関連する課題の研究
- URL
- http://academic.oup.com/ptep/article-pdf/2019/7/073A01/28914433/ptz057.pdf
- ID情報
-
- DOI : 10.1093/ptep/ptz057
- eISSN : 2050-3911
- arXiv ID : arXiv:1903.05944