市场动力学原理——经济动力学与标准模型(Ⅱ)  

Principles of Market Dynamics:Econ-dynamics and Standard Model(Ⅱ)

作　　者：杨英锐 Yingrui Yang(Department of Cognitive Science,Rensselaer Polytechnic Institute Troy,New York 12180,USA)

机构地区：[1]美国伦斯勒理工学院认知科学系

出　　处：《科学．经济．社会》2023年第1期95-128,共34页Science Economy Society

摘　　要：市场动力学以经典电动力学为基础,以量子电动力学为参考模型框架,其构造自始至终贯穿布尔巴基结构主义思想。市场动力学研究价格、需求和供给三者之间的相互作用,量子电动力学研究光子、电子和正电子三者之间的相互作用;两者都属于单荷动力学范畴,共享U(1)对称群。市场动力学引入了市场荷,并以此分别定义了需求与供给。通过考察市场犹豫现象,为需求和供给引入自旋作为其内禀性质。于是,需求与供给可由狄拉克旋量定义。通过引入钱锥和价壳,定义了虚价格;需求与供给通过交换虚价格而相互作用。这些相互作用可为费曼图所刻画。认知场具有极化决策的功能,由磁场所刻画。市场动力学认为,社会经济本身是一个实验,每个市场参与者都是观测者。我们建立了市场观测的非对易关系以及观测信息的市场版测不准原理,并以此定义了量子版看不见的手。在经典电动力学的基础上,讨论了价格场与麦克斯韦场的关系,并引入了规范势的概念。高阶认知(包括博弈、决策与推理)引起的市场涨落(包括介观与量子涨落)。各种市场内在的涨落现象既是理解市场参与者认知又是理解市场相变的基础。定义了市场波函数的六个组分,即全局相因子,全局规范势与全局规范场强,以及局域相因子,局域规范势与局域规范场强。规范变换是量子电动力学和市场动力学的精彩部分,随后给出规范原理,说明全局对称性是局域对称性的必要条件。引入了四个算子,即牛顿均值算子、爱因斯坦钱锥算子、薛定谔演化算子和狄拉克场论算子,将这四个算子分别施用于市场波函数,呈现市场波函数的四种算子相态;算子态的改变,称为市场波函数的相变。Market dynamics is constructed by taking classical electrodynamics as a base, and using quantum electrodynamics as a referential modeling framework. The constructing process follows the Bourbaki structuralism approach. Market dynamics studies the interactions of price, demand, and supply. Quantum electrodynamics studies the interactions of photon, electron, and positron. Both belong to the category of single-charge dynamics and share the U(1) symmetry group. Market dynamics introduced the notion of market charge, and by doing so redefined demand and supply. Observe the hesitation phenomenon on the market as an intrinsic property, introducing the spin of demand and supply, such that together they can be characterized by Dirac spinor. We define the virtual price by introducing the money-cone and the priceshell. The interactions between demand and supply consist of exchanging virtual prices, which can be described by Feynman diagrams. Modeled by a magnetic field, cognitive field functions to polarize decisions. Market dynamics regards the social economy itself as an experiment, and thus each and every market participant is an observer. We established the non-commutative law of market observations, and formulated the market version of the uncertainty principle;further defined the quantum version of the invisible hand. Based on the classical electrodynamics, the relations of price field and Maxwell field are discussed and the notion of vector potential was introduced. High cognition(including reasoning, game theory, decision making, and reasoning) causes market fluctuations(including classical, mesoscopic, and quantum fluctuations). Investigations of market fluctuations are fundamental for understanding market participants’ cognition and market phase changes. We defined the six components of market wave function, including the global phase factor, global gauge potential, global field strength, as well as the local phase factor, local gauge potential, and local gauge field strength. Gauge transformation is a beautifu

关 键 词：市场荷 价格 需求 供给 自旋 波函数 规范变换 对称群 看不见的手 非对易关系 市场涨落 狄拉克算子 

分 类 号：B089[哲学宗教—哲学理论]