共查询到19条相似文献,搜索用时 335 毫秒
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本文较详细地给出物理上的规范场与数学上的主纤维丛上的联络论之间的对应关系,从而以联络论的观点统一地处理杨振宁所说的规范场的“微分方法”与“积分”方法,并指出存在有更广泛的规范场的可能性。此外,讨论了引力场如何作为规范场及比较了一些已知的引力场方程。 相似文献
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通过研究一半整数自旋值的中性粒子在球对称磁场中的Born-Oppenheimer方程,发现在自旋空间Berry联络呈非阿贝尔形式.在绝热近似下,Berry联络相当于阿贝尔形式的吴-杨单极场.由于拓扑的非平庸性,利用纤维丛中截面的概念研究了位形空间的动力学,发现中心势场中粒子的角动量和能量均取量子化值,但数值发生移动,这是纯几何起源的现象. 相似文献
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本文讨论了时空上deRham与联络空间的水平变更或与联络空间垂直变更构成的双上同调系列间的关系以及与族指数定理的关系。
关键词: 相似文献
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通过研究一半整数自旋值的中性粒子在球对称磁场中的Born-Oppenheimer方程,发现在自旋空间Berry联络呈非阿贝尔形式.在绝热近似下,Berry联络相当于阿贝尔形式的吴-杨单极场.由于拓扑的非平庸性,利用纤维丛中截面的概念研究了位形空间的动力学,发现中心势场中粒子的角动量和能量均取量子化值,但数值发生移动,这是纯几何起源的现象. 相似文献
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在AdS5S5背景中,IIB超弦的运动方程与Maurer-Cartan方程在世界面上存在对偶对称性.通过引入扭曲对偶(twisteddual)的概念,将有限的对偶变换推广到连续的对偶变换,并给出了AdS5S5中IIB超弦的Lax联络及其可积的相容条件.
关键词:
扭曲对偶
κ对称性
Lax联络 相似文献
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从Rahmfeld和Rajaraman构造的在AdS3×S3背景中具有κ对称的GS弦的作用量出发, 推导出AdS3×S3弦的运动方程, 然后利用连续的扭曲对偶变换构造了带有自由参数λ的平联络, 利用这些平联络可进一步得到无穷多守恒量, 说明此系统是可积的. 相似文献
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本文采用几何学方法将含碎裂机制的广义凝结方程表述为一个赋予仿射联络的无限维空间中的代表点的测地线运动方程. 相似文献
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双棒串接Nd3+:YAG激光器 总被引:4,自引:2,他引:2
根据测量的单根Nd3+:YAG棒的热焦距,利用ABCD传输矩阵计算了双棒串接的几种腔型的稳定参量,给出了能够满足高功率、高稳定性激光输出的稳定腔型,实验结果与理论分析基本相符. 相似文献
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干涉和衍射的联系与区别 总被引:1,自引:0,他引:1
通过理论分析得出双缝实验中空间光场的分布是干涉与衍射共同作用的结果.在形成条件、分布规律以及数学处理方法上说明了干涉和衍射的区别与联系. 相似文献
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介观二阶并联电路的量子涨落 总被引:3,自引:0,他引:3
从有源RLC并联电路的经典运动方程出发,通过引入复正则变量,提出了RLC并联电路的量子化方案.作为应用,研究了压缩真空态下介观并联RLC电路中电压,电流的量子涨落,并对结果进行了讨论. 相似文献
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A. Rod Gover Petr Somberg Vladimír Souček 《Communications in Mathematical Physics》2008,278(2):307-327
Working over a pseudo-Riemannian manifold, for each vector bundle with connection we construct a sequence of three differential
operators which is a complex (termed a Yang-Mills detour complex) if and only if the connection satisfies the full Yang-Mills
equations. A special case is a complex controlling the deformation theory of Yang-Mills connections. In the case of Riemannian
signature the complex is elliptic. If the connection respects a metric on the bundle then the complex is formally self-adjoint.
In dimension 4 the complex is conformally invariant and generalises, to the full Yang-Mills setting, the composition of (two
operator) Yang-Mills complexes for (anti-)self-dual Yang-Mills connections. Via a prolonged system and tractor connection
a diagram of differential operators is constructed which, when commutative, generates differential complexes of natural operators
from the Yang-Mills detour complex. In dimension 4 this construction is conformally invariant and is used to yield two new
sequences of conformal operators which are complexes if and only if the Bach tensor vanishes everywhere. In Riemannian signature
these complexes are elliptic. In one case the first operator is the twistor operator and in the other sequence it is the operator
for Einstein scales. The sequences are detour sequences associated to certain Bernstein-Gelfand-Gelfand sequences. 相似文献
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Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which we call the exterior dimension. In addition, it is shown that the exterior dimension is related to the “uncertainty exponent” previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted. 相似文献
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Mark A. Mostow 《Communications in Mathematical Physics》1980,78(1):137-150
We show that a connection of a principal bundle is determined up to (global) gauge equivalence by the curvature and its covariant derivatives provided that the infinitesimal holonomy group is of constant dimension and the base space is simply connected. If the dimension of the infinitesimal holonomy group varies, there may be obstructions of a topological nature to the existence of a global or even local gauge equivalence between two connections whose curvatures and covariant derivatives of curvature agree everywhere. These obstructions are analyzed and illustrated by examples. 相似文献
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Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations
We explore the ultraviolet continuum regime of causal dynamical triangulations, as probed by the flow of the spectral dimension. We set up a framework in which one can find continuum theories that can in principle fully reproduce the behavior of the latter in this regime. In particular, we show that, in 2 + 1 dimensions, Ho?ava-Lifshitz gravity can mimic the flow of the spectral dimension in causal dynamical triangulations to high accuracy and over a wide range of scales. This seems to provide evidence for an important connection between the two theories. 相似文献