修改后的 CKP 层次结构的 Tau 功能

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-11-13 DOI:10.1016/j.geomphys.2024.105367

Shen Wang , Wenchuang Guan , Jipeng Cheng

引用次数: 0

摘要

修正 CKP（mCKP）层次结构是一种重要的可积分层次结构，它通过 Miura 链接与 CKP 层次结构相关。研究证明，mCKP 层次结构存在一个 tau 对（τ0,τ1）。我们进一步发现，mCKP 层次结构可以完全由 CKP tau 函数和相应的 CKP 特征函数决定。在此基础上，我们通过 CKP 达布变换构建了 mCKP tau 函数，并给出了自由玻色子的真空期望值。作为副产品，我们还推导出了〈1|eH(to)β0eβn22eβn-122⋯eβ122g|0〉的行列式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Tau functions of modified CKP hierarchy

Modified CKP (mCKP) hierarchy is an important integrable hierarchy, that is related to CKP hierarchy through Miura link. It has been proven that there exists a tau pair

(τ_{0}, τ_{1})

for mCKP hierarchy. Further we find that mCKP hierarchy can be fully determined by CKP tau function and corresponding CKP eigenfunction. Based on this, we construct mCKP tau functions by CKP Darboux transformations and also present the vacuum expectation value of free bosons. As a byproduct, determinant formula for

〈 1 | e^{H (t_{o})} β_{0} e^{\frac{β_{n}^{2}}{2}} e^{\frac{β_{n - 1}^{2}}{2}} \dots e^{\frac{β_{1}^{2}}{2}} g | 0 〉

is also derived.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity