Stochastical Mechanics of Particle Systems in Clifford-Analytical Formulation Related to Hurwitz Pairs of Bidimension (8,5)
Stochastical Mechanics of Particle Systems in Clifford-Analytical Formulation Related to Hurwitz Pairs of Bidimension (8,5)
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与二维 Hurwitz 对相关的 Clifford 解析公式中粒子系统的随机力学 (8,5)
DOI：
10.1007/978-94-011-1896-5_10
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
O. Suzuki
中科院分区：
文献类型：
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作者：
J. Ławrynowicz;L. Wojtczak;S. Koshi;O. Suzuki
粒子系统被认为是嵌入多维空间中的相互作用粒子的系统。通常的单粒子时空可以被视为至少五维空间的投影，其中第五维具有随机特征。提出了五维经典力学的公式，这是由于第五维出现而导致的相对论力的非平凡概括。 — 引入的五维几何简化了更复杂的 Grauert 几何，并根据五维和八维伪欧几里得 Hurwitz 对的广义 Hurwitz 问题的可解性，确保正确的 Clifford 代数和相应的类狄拉克方程的分析。因此，相应的全纯映射使我们能够构建描述经典、量子和统计力学中所需的粒子行为的旋量。 — 在统计力学中，多维几何的描述自然地导致热力学变量波动的出现。我们对问题的表述是基于扩展到多体形式的类狄拉克方程，即从五维和八维空间对开始推广到几代赫尔维茨对的布赖特构造。该构造导致第二量化表示中的哈密顿量，其系数包含随机参数。 — 通常的对角化过程使我们能够找到电子或原子特征向量的能量特征值和振幅。然后区分垂直于表面的方向，并且特征向量具有驻波特征。正确选择边界条件可以保证系统的稳定性。本卷中发表的 B. Gaveau、J. Ławrynowicz 和 L. Wojtczak 的论文给出了一个说明性的例子。
A particle system is considered a system of interacting particles embedded in a many-dimensional space. The usual one-particle space-time may then be treated as a projection of an at least five-dimensional space, where the fifth dimension is of stochastic character. A formulation of the clasical mechanics infivedimensions is proposed, which is a non-trivial generalization of the relativistic forces as a result of the appearance of the fifth dimension. — The five-dimensional geometry introduced simplifies a more sophisticated Grauert geometry and assures the proper Clifford algebras and analyses of the corresponding Dirac-like equations according to the solvabilty of the generalized Hurwitz problems for the pseudo-euclidean Hurwitz pairs of dimensions five and eight. Therefore the corresponding holomorphic mappings enable us to construct spinors which describe the behaviour of particles as needed in the classical, quantum and statistical mechanics. — In the statistical mechanics the description in terms of a many-dimensional geometry leads in a natural way to the appearance of fluctuations of thermodynamical variables. Our formulation of the problem is based on Dirac-like equations extended to many-body forms, i.e. the Breit construction generalized to the generations of Hurwitz pairs starting from the pairs of spaces of dimensions five and eight. The construction leads to the hamiltonian in the representation of second quantization whose coefficients contain the stochastical parameters. — The usual diagonalization procedure allows us to find the energy eigenvalues and amplitudes of electronic or atomic eigenvectors. The direction perperdicular to the surface is then distinguished and the eigenvectors are of standing-wave character. The stability of the system is assured by a proper choice of boundary conditions. An illustrative example is given in the paper by B. Gaveau, J. Ławrynowicz and L. Wojtczak, published in this volume.
S. Yamashita、N. Sakai、Y. Matsuzawa 等人：“与胆固醇酯转移活性完全缺乏相关的家族性高 α-脂蛋白血症的临床和生化特征。”
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