p-adic开、闭和开闭弦的非线性方程

关于Adelic弦

On Adelic Strings

考虑到不仅世界单而且闵可夫斯基时空和弦动量都可以是p-adic和adelic的，提出了一种新的p-adic弦和adelic弦的方法。p-Adic和adelic弦振幅被认为是在费曼的路径积分形式主义。计算了阿德利克·韦内齐亚诺振幅。得到弦动量的某些离散性。此外，阿德利克耦合常数等于1。

Regularization of p-adic String Amplitudes, and Multivariate Local Zeta Functions

We prove that the p-adic Koba-Nielsen type string amplitudes are bona fide integrals. We attach to these amplitudes Igusa-type integrals depending on several complex parameters and show that these integrals admit meromorphic continuations as rational functions. Then we use these functions to regularize the Koba-Nielsen amplitudes. As far as we know, there is no a similar result for the Archimedean Koba-Nielsen amplitudes. We also discuss the existence of divergencies and the connections with multivariate Igusa's local zeta functions.

Minkowski dimension and explicit tube formulas for $p$-adic fractal strings

The local theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) of fractal strings. Such geometric oscillations can be seen most clearly in the explicit volume formula for the tubular neighborhoods of a $p$-adic fractal string $\mathcal{L}_p$, expressed in terms of the underlying complex dimensions. The general fractal tube formula obtained in this paper is illustrated by several examples, including the nonarchimedean Cantor and Euler strings. Moreover, we show that the Minkowski dimension of a $p$-adic fractal string coincides with the abscissa of conv…

标量快子场的$p$ -adic开弦方程

On the equation of the $p$-adic open string for the scalar tachyon field

研究了标量快子场$p^{\frac12\partial^2_t}Φ=Φ^p$中描述$p$ -adic开弦动力学的一维非线性伪微分方程解的结构。我们引出的作用，真正的零的整个功能$Φ^p(z)$和行为的解决方案$Φ(t)$在这些零的附近。指出当$p$为偶数时，会出现不连续解.我们使用的方法展开的解决方案$Φ$和功能$Φ^p$的Hermite多项式和修改的Hermite多项式，并建立这些展开（积分守恒律）的系数之间的联系。对于$p=2$，我们构造了一个未知Hermite系数的无限非线性方程组，并研究了它的结构。我们考虑3-近似。我们指出的问题和热方程的非线性边值问题之间的连接。

p-进弦理论中的非线性动力学方程

On the Nonlinear Dynamical Equation in the p-adic String Theory

研究p-进弦理论中出现的含无穷阶导数的非线性伪微分方程，证明了缓增分布代数中的唯一性定理，并分析了有界解、空间齐次解及孤立子和q-膜解的存在性。

p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field

We establish rigorously the regularization of the p-adic open string amplitudes, with Chan-Paton rules and a constant B-field, introduced by Ghoshal and Kawano. In this study we use techniques of multivariate local zeta functions depending on multiplicative characters and a phase factor which involves an antisymmetric bilinear form. These local zeta functions are new mathematical objects. We attach to each amplitude a multivariate local zeta function depending on the kinematics parameters, the B-field and the Chan-Paton factors. We show that these integrals admit meromorphic continuations in t…

弦模型中的非定域瞬子和孤子

Nonlocal instantons and solitons in string models

研究了一类可以用在辅助径向维上扩散的局域标量场描述的非局域系统。作为例子p进，开放和边界弦场论被认为是闵可夫斯基，弗里德曼-罗伯逊-沃克和欧几里德度量背景。从几乎处处为常数的类分布初始场出发，构造了非局部解的精确解和近似解。欧几里德p-adic块被解释为孤子膜，而超对称开弦场论的欧几里德扭结被解释为瞬子。不同的弦论的解决方案之间的一些关系也突出了由于重新制定的非局部系统作为一个重整化群流的不动点。

Zeta非局部标量场

Zeta Nonlocal Scalar Fields

我们考虑了一些起源于p-adic弦论的非定域非多项式标量场模型。无穷多个时空导数由算符值Riemann zeta函数通过d 'Alembertian $\Box$确定。从p进快子弦有效场的精确拉格朗日量$\mathcal{L}_p$出发构造相应的拉格朗日量L，将其推广为用任意自然数n代替p，然后对所有n取$\mathcal{L}_n$的和.对应的新对象我们称之为zeta标量弦。本文得到并给出了这些场的一些基本经典场性质。特别地，研究了运动方程的某些解及其快子谱。具有黎曼zeta函数动力学的场论本身也很有趣。

量子开闭同伦代数与弦场论

Quantum Open-Closed Homotopy Algebra and String Field Theory

我们用同伦代数重新表述了兹维巴赫量子开闭弦场论的代数结构。我们称之为量子开闭同伦代数（QOCHA），它是Kajiura和Stasheff的开闭同伦代数（OCHA）的推广。同伦公式揭示了闭弦背景对开弦场论变形的新认识。特别是，量子闭同伦代数的毛雷尔嘉当元素的变形定义了相容的量子开弦场论。

玻色弦场论的同伦分类

Homotopy Classification of Bosonic String Field Theory

证明了量子闭弦场论的圈同伦代数的分解定理，并利用它证明了在给定弦背景和给定S-矩阵上，闭弦场论在规范变换下是唯一的.对于开弦和闭弦的理论，我们使用开闭同伦代数的结果来证明不等价的开弦场论空间与经典闭弦背景空间是同构的。作为开闭同伦代数的进一步应用，我们证明了弦场论是背景独立的，并且在非常精确的意义下是局部唯一的。最后，我们在同伦代数的框架下讨论了拓扑弦论，并找到了闭弦和开弦场论之间的一个广义对应。

KLT Factorization of Winding String Amplitudes

We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.

关于取$p$-adic值的波函数的路径积分

On path integrals for wave functions taking $p$-adic values

本文通过$p$-adic多重积分构造了描述取$p$-adic值波函数演化的路径积分，并计算了自由粒子的费曼传播子，结果与经典情况相似。