arXiv 0809.46922008-09-28hep-th

交换作用与相对论薛定谔理论中的最小能量原理

Exchange Interactions and Principle of Minimal Energy in Relativistic Schroedinger Theory

M. Mattes, M. Sorg

备注：: 110 pages, 1 figure

摘要：

在前面的论文中为非全同粒子（例如电子偶素）系统建立的最小能量原理，现在也被推广到全同粒子。由于后一种粒子也感受到交换力（除了通常的电磁力之外），根据相对论薛定谔理论的非阿贝尔特征，人们必须处理非零交换势，这使得理论非线性。然而，目前的变分原理的扩展只涉及线性化的版本，以保持足够简单的计算。证明了狄拉克粒子在量子力学中可以处于费米子量子态和玻色子量子态，并验证了变分原理在两种量子态（具体为费米子氢态2p_3/2和玻色子正电子偶素态2^1P_1）的数学和物理一致性.

英文摘要：

The principle of minimal energy, which has been set up in the preceding papers for systems of non-identical particles (e.g. positronium), is now generalized to include also identical particles. Since the latter kind of particles feels also the exchange forces (besides the usual electromagnetic forces), one has to deal with non-zero exchange potentials which render the theory nonlinear, according to the non-Abelian character of Relativistic Schroedinger Theory (RST). However, the present extension of the variational principle refers only to the linearized version of RST in order to keep the calculations sufficiently simple. It is also demonstrated that in RST the Dirac particles can occur in fermionic and bosonic quantum states; and the mathematical and physical consistency of the variational principle is validated for both types of states (concretely the fermionic hydrogen state 2p_3/2 and the bosonic positronium state 2^1P_1).

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摘要：

英文摘要：

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