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Distribution of Energy Momentum Tensor around Static Charges in Lattice Simulations and an Effective Model

柳原, 良亮 大阪大学 DOI:10.18910/82006

2021.03.24

概要

エネルギー運動量テンソル(EMT)は物理学における最も基本的な観測量の1つである。近年、勾配流と呼ばれる手法に基づく全く新しいEMTの解析法が提案され、格子ゲージ理論においても適切にEMTを定義できることが示された。これを受け、勾配流法に基づくEMTを用いた熱力学量の格子数値解析が行われ、この解析手法の有用性が実証された。

 本研究では、勾配流法を用いてSU(3)Yang-Mills(YM)ゲージ理論に基づく格子数値計算を行い、静的電荷が存在する非一様系でのEMT分布を解析した。静的電荷はSU(3)YMゲージ理論のような複雑な量子系を探索するためのプローブの役割を担う。このときEMTは静的電荷に対する系の局所的な応答を特徴づけ、非摂動現象に対する重要な知見を与える。さらに本研究では、可換Higgs(AH)模型と呼ばれる有効模型を用いてEMT分布を解析し、格子数値解析の結果との比較も行った。

 本論文では、まずSU(3)YMゲージ理論の非閉じ込め相における1体クオーク周辺のEMT分布に対する格子数値解析を行った。連続極限までとった解析で得られたEMT分布は、古典電磁気学や有限温度場の理論に基づくLeading­order(LO)の計算結果とは明確な違いを示すということを明らかにした。またEMT分布の近距離のふるまいに着目し、摂動論のLOの結果と比較することで強い相互作用の結合定数の情報を抜き出した。一方で、長距離の振る舞いは媒質による熱遮蔽効果を示唆していることを見出した。

 次にSU(3)YMゲージ理論の真空に目を向け、静的クオーク•反クオーク(QQ⁻)の周辺でのEMT分布を格子数値解析により調べた。真空では系の力の伝搬がフラックスチューブと呼ばれる1次元的構造に集約される様相を、ゲージ不変なEMT分布として描き出すことに成功した。またEMTの横方向の分布が、可換理論の結果とは質的に全く異なるということを定量的に明らかにした。さらに解析の整合性を確認するために、QQ⁻ポテンシャルの微分とEMTの空間成分の積分からそれぞれ定義される力が一致することを示した。

 最後に、フラックスチューブ周辺の局所的空間構造をさらに調べるために、保存則およWH模型に基づき、QQ⁻系のEMT分布を解析した。EMTが満たす保存則に着目すると、上の第一原理計算で得られた結果は、QQ⁻間距離が有限であることの重要性を強く示唆していることが分かった。そこでAH模型に基づき、無限長および有限長の磁気渦糸周辺のEMT分布を調べ、双対超伝導の観点から格子数値解析の結果と比較した。格子計算の結果を再現するAH模型のパラメータは、広範にわたって存在しないことを明らかにした。

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