arXiv quant-ph/04111752004-11quant-ph

事件的量子力学理论的基本概念

Basic Concepts for a Quantum Mechanical Theory of Events

Kim J. Bostroem

备注：: 48 pages, 4 figures, revised introduction, minor corrections

摘要：

一个物理理论被提出来，它同时遵守狭义相对论和量子力学的原理。作为一个关键特征，这些定律是根据量子事件而不是粒子状态来制定的。量子事件的时间和空间坐标被平等对待，即作为希尔伯特空间上的自伴算子。该理论不是基于拉格朗日或哈密顿力学，并打破了连续流动时间的概念。所考虑的物理对象是暴露于外部电势的无自旋粒子。该理论也解释了粒子-反粒子对的产生和湮灭，因此不是通常意义上的单粒子理论。麦克斯韦方程组作为某些基本对易关系的直接结果而导出。在非相对论性极限和时间不确定性消失的极限下，得到了无自旋粒子在外电磁场作用下的薛定谔方程。

英文摘要：

A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial coordinates of a quantum event are treated on equal footing, namely as self-adjoint operators on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics, and breaks with the concept of a continuously flowing time. The physical object under consideration is a spinless particle exposed to an external potential. The theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the usual sense. The Maxwell equations are derived as a straightforward consequence of certain fundamental commutation relations. In the non-relativistic limit and in the limit of vanishing time uncertainty, the Schrödinger equation of a spinless particle exposed to an external electromagnetic field is obtained.

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