Representations of the Poincaré Semigroup and Relativistic Causality

This paper provides the mathematical tools for addressing issues of two kinds of causality in relativistic scattering theory: general causality, i.e., an effect can only be measured after its cause, and Einstein causality, i.e., no propagation of probability outside of the forward light cone. Starting from Wigner's unitary irreducible representations of the Poincaré group for noninteracting, one particle states, we describe the mathematical tools necessary to describe scattering states, the Lippmann-Schwinger Dirace kets, and to describe resonances and decaying states, the relativistic Gamow ket. An important step for their derivations is the Hardy space hypothesis. Investigating the transformation properties of scattering and resonance states under the dynamical Poincaré semigroup reveals that both kinds of causality result from this hypothesis about nature of the spaces of states and observables.     

基于格兰杰因果网络的中美贸易战对上证行业冲击的研究

中美贸易战对行业冲击是普遍关注的问题,本文选取2016年8月—2019年10月的上证行业指数,构建了格兰杰因果关系网络,然后结合事件分析法对风险传播模型的参数进行估计,最后利用蒙特卡罗算法模拟行业受到贸易战冲击后金融风险传播情况,并计算贸易战发生前后的上证股市金融网络风险传播的基本再生数.研究发现:第一,贸易战明显改变了上证行业关系结构,行业指数之间联系变得更为紧密;第二,贸易战发生初期,受美国加征关税影响,上证股市感染节点数量迅速增加,并且感染规模会在第10—15个交易日内达到峰值,感染节点数量大约在第25个交易日后开始趋于平缓,市场逐渐恢复;第三,基本再生数计算结果表明,上证股市在贸易战发生初期金融风险传播较快,上证股市容易产生“同涨同跌”的现象.     

改进BP神经网络及其在陕西就业预测中的应用

就业是一个非常重要的社会和经济统计指标.世界各国政府都非常重视就业问题,将增加就业率作为政府的工作目标.要想解决就业矛盾,就应该对就业问题的未来发展趋势有一个清醒的认识,从而做出正确的决策.本文提出了一种基于因果关系理论、协整理论用于控制与预测的改进BP神经网络,并将其应用于陕西省就业的控制和预测中.     

粮食价格与居民消费价格关系的统计分析——1997.1—2005.4年粮价与物价的实证分析

通过对粮价与物价的格兰杰检验,给出粮价与物价就统计意义上的因果关系.并考虑到物价和粮价可能存在集群性,对粮价和物价建立误差修正-自回归条件异方差混合模型.     

中国人口增长与粮食生产的协整研究

本文以1978-2004年为样本数据,对中国人口和粮食产量进行了单位根检验、协整检验和Granger因果关系检验.结果表明,样本期内人口因素不是粮食生产的Geanger原因,人口增长和粮食生产发展并不协调.通过建立中国粮食生产模型,预测了2006-2010年的人口增长与粮食生产趋势,提出了实现中国人口增长与粮食生产和谐发展的几点建议.     

城镇登记失业率影响因素的探讨

就城镇登记失业率的相关问题进行了研究.利用格兰杰因果关系检验解决了确定影响因素的问题;建立了主成分分析模型和基于序列相关性的误差修正模型,解决了各影响因素和城镇登记失业率之间关联的问题;并利用所建模型对未来我国的就业前景作出仿真预测,得出了相应结论.     

Ten years of the analytic perturbation theory in QCD

The renormalization group method allows improving the properties of the QCD perturbative power series in the ultraviolet region. But it ultimately leads to unphysical singularities of observables in the infrared domain. The analytic perturbation theory is the next step in improving the perturbative expansions. Specifically, it involves an additional analyticity requirement based on the causality principle and implemented in the Källen-Lehmann and Jost-Lehmann representations. This approach eliminates spurious singularities of the perturbative power series and enhances the stability of the series with respect to both higher-loop corrections and the choice of the renormalization scheme. This paper is an overview of the basic stages in developing the analytic perturbation theory in QCD, including its recent applications to describing hadronic processes.     

An analysis of the validity of local causality at the statistical level in Einstein-Podolsky-Rosen-Type situations

We investigate the question of local causality at the statistical level in Einstein-Podolsky-Rosen (EPR) type situations, taking into account the most general class of measurements envisaged in quantum theory. The condition for local causality at the statistical level used in this paper pertains to the invariance of statistics of measurements on one sub-system with respect to the choice and type of measurements on its correlated partner in the EPR-type examples. Our analysis is based on a criterion for measurements performed on one of the EPR sub-systems, which is more general than the criterion used in the earlier treatments. We discuss both non-absorptive measurements (where the system is available for further observation after the measurement is performed) as well as absorptive measurements (where the system is absorbed in the process of a particular outcome being realized). We show that in the case of arbitrary non-absorptive measurements characterized by operationvalued measures, the requirement of local causality at the statistical level is satisfied and in the process we identify the key inputs in such a proof. We also obtain the specific conditions under which an absorptive measurement satisfies local causality at the statistical level.