论文标题
量子理论的重新制定
Reformulation of Quantum Theory
论文作者
论文摘要
我们首先回想起一个事实，在数学物理学家中众所周知，尽管在理论物理学家中鲜为人知，即复杂的希尔伯特空间上的标准量子力学是一种哈密顿力学，是关于希尔伯特（Hilbert）空间作为线性真实歧管，配备了其规范性的符号形式，并且仅限制了预期的象征性函数的象征性形式。然后，在此框架中，我们以符合歧管的语言重新制定了量子力学的结构，并避免了希尔伯特空间的线性结构，以使结果可以指定为任意的符号歧管。
We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert space as a linear real manifold equipped with its canonical symplectic form and restricting only to the expectation-value functions of Hermitian operators. Then in this framework, we reformulate the structure of quantum mechanics in the language of symplectic manifolds and avoid linear structure of Hilbert space in such a way that the results can be stated for an arbitrary symplectic manifold.
