Methods in quantum field theory and their applications

量子场论方法及其应用

• 批准号: 09640339
• 负责人: FUJIKAWA Kazuo
• 金额: $ 1.86万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640339/
• 关键词: membrane theory; Lorentz covariance; matrix regularizaion; BRST symmetry; lattice gauge theory; Dirac operator; Ginsparg-Wilson relation; ゲージ理論; ゲージ固定; カスラル変換; 量子異常; 量子化; 経路積分; 揺動散逸定理; トンネル効果; カイラル対称性; 超対称性; 弦理論

We first investigated the quantum theory of membranes. The membrane is an extension of string theory and it is expected to play a fundamental role in the formulation of the so-called M theory. In this connection, the matrix formulation of the membrane is important. In the past formulation of the matrix regularization of the membrane, the lightcone gauge has been used. In our approach, we studied to what entent a Lorentz covariant matrix regularization of the membrane is possible. We have shown that the Bosonic membrane can be formulated as a matrix theory except for a subtle property related to the Faddeev-Popov ghost. As for a supersymmetric membrane, we encountered a more fundamental complication, which may be solved only when we formulate it in a way completely different from the present formulation of membrane.We have recently witnessed a remarkable progress in the treatment of lattice fermion operators. We clarified the meaning of index theorem on the lattice and the physical meaning of the new fermionic operator. More recently, we have extended the so-called Ginsparg-Wilson relation to a form characterized by non-negative integers. It was shown that these new lattice Dirac operators are free of species doubling and satisfy the correct form of index theorem in the smooth continuum limit.

我们首先研究了膜的量子理论。膜是弦理论的延伸，它有望在所谓的M理论的形成中发挥基本作用。在这方面，膜的基质配方是重要的。在过去的膜矩阵正则化公式中，采用了光锥规。在我们的方法中，我们研究了膜的洛伦兹协变矩阵正则化在多大程度上是可能的。我们已经证明，玻色子膜可以表述为一个矩阵理论，除了一个微妙的性质有关的Faddeev-Popov鬼。至于超对称膜，我们遇到了一个更基本的复杂问题，只有当我们用一种完全不同于目前膜的表述方式来表述它时，这个问题才能得到解决。我们最近在处理晶格费米子算符方面取得了显著的进展。阐明了格上指标定理的意义和新费米算子的物理意义。最近，我们把所谓的金斯帕尔-威尔逊关系推广到以非负整数为特征的形式。证明了这些新的点阵狄拉克算子不存在种加倍，并且满足光滑连续体极限下指标定理的正确形式。

项目成果

K.Fujikawa et.al: "An extended q-deformed su (2) algebra and the Bloch electron problem"Phys.Lett.. A239. 21-26 (1998)

K.Fujikawa 等人：“扩展的 q 变形 su (2) 代数和布洛赫电子问题”Phys.Lett.. A239。

K.Fujikawa: "Fluctuation-dissipation theorem and quantum tunneling with dissipation"Phys.Rev.. E57,No 5. 5023-5029 (1998)

K.Fujikawa：“涨落耗散定理和耗散量子隧道”Phys.Rev.. E57，No 5. 5023-5029 (1998)

K.Fujikawa: "Relation Trγ5=0 and the index theorem in lattice gauge theory"Phys.Rev.. D60. 074505-16 (1999)

K.Fujikawa：“关系式 Trγ5=0 和格子规范理论中的指数定理”Phys.Rev.. D60 (1999)。

K.Fujikawa et.al: "Duality in potential curve crossing: Application to quantum coherence"Phys.Rev.. A56,No 5. 3436-3445 (1997)

K.Fujikawa 等人：“势曲线交叉中的对偶性：在量子相干性中的应用”Phys.Rev.. A56，No 5. 3436-3445 (1997)

K.Fujikawa: "Algebraic generalization of the Ginsparg-Wilson relation"Nucl.Phys.. B589. 487 (2000)

K.Fujikawa：“Ginsparg-Wilson 关系的代数推广”Nucl.Phys.. B589。