量子力学的公理化

我们提出的量子力学唯一公理是：普朗克能量等于爱因斯坦能量：h·v=E=m·c2用纯文字来表达就是：频率与能量等价——因为大自然并不理会单位制的选择。广义相对论并没有把选用何种数学工具列入公理，本文也然。公理化方案的优点是：既然公理是可信和可理解的，那么公理的一切推论也都是可信和可理解的，最终的判决是实验。大道至简。我们遵守“奥卡姆剃刀”原则。在量子力学的语境中每一个物理量都必须而且能够重新定义，即使仍然使用同样的词。量子化替换是公理化的推论。历来的讲法是：量子力学的数学基础是Hilbert空间理论。而我们认为量子力学的数学基础是Hilbert空间的群表示论。区别在于，实验物理学家生活在4度时空，而群表示论是4度时空与Hilbert空间之间的桥梁。

Axiomatization of Quantum Mechanics

The unique principle we propose as the fundamental of quantum mechanics is： Planck energy is equal to Einstein energy. In other words, frequency is equivelent to energy because Nature does not mind which unit system is chosen. In the axioms of general relativity, Einstein did not declare which mathematic tool must be used, we follow him in our case. Because axioms are convincible and under- standable, as well as all their inferences, the final justification is experiment. The first principle is most brief and simple. We obey the principle of ＂Occam razor＂. In the context of quantum mechanics every physical observable must be and can be redefined even we keep using the same word. Quantization is the inference of axiomation. Conventional opinion is that ＂the mathematical foundation of quantum mechanics is the theory of Hilbert space＂. In our opinion, the mathematical foundation of quantum mechanics is the theory of group representation of Hilbert space. The difference is, experimental physicists are living in 4-dimensional space-time, and the theory of group representation connects Hilbert space and 4-dimensional space-time.