相对论性量子力学的因果网方法
A Causal Net Approach to Relativistic Quantum Mechanics
摘要：
在本文中，我们讨论了因果网络的方法来描述相对论性量子力学。因果网络上的每个顶点代表一个可能的点事件或粒子观察。通过在适当的时间构造基于类Reichenbach合取叉的最简单因果网，我们可以精确地导出相对论费米子的1+1维Dirac方程，并正确地模拟量子力学统计。网络的对称性提供了各种量子力学效应，如量子不确定性和波函数，相位，自旋，负能态和势的影响。因果网络可以嵌入3+1维空间，并且与传统的狄拉克方程一致。在低速极限下，因果网近似于电磁场的薛定谔方程和泡利方程。扩展到不同的动量状态，该网络与量子力学的费曼路径积分方法兼容，该方法允许计算众所周知的量子现象，如衍射。
英文摘要：
In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrodinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.
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