推广了D. S. Shirokov关于维数为$2^n$的实Clifford代数或复Clifford代数的两组反交换元的一个定理，推广到两组反交换元光滑依赖于维数为$r$的欧氏空间的点的情形.证明了在偶$n$情形下，存在一个光滑函数使得两个Clifford代数元素集通过相似变换连接.在奇$n$的情况下，考虑两个集合之间的连接的所有情况。利用一般形式的自旋联系方程，证明了局部泡利定理的问题等价于某些特殊的偏微分方程组的解的存在性问题。详细考虑了问题的特殊情况$n=2$，$r\geq 1$和具有更简单解的$n\geq 2$，$r=1$.
英文摘要：
Generalized Pauli's theorem, proved by D. S. Shirokov for two sets of anticommuting elements of a real or complexified Clifford algebra of dimension $2^n$, is extended to the case, when both sets of elements depend smoothly on points of Euclidian space of dimension $r$. We prove that in the case of even $n$ there exists a smooth function such that two sets of Clifford algebra elements are connected by a similarity transformation. All cases of connection between two sets are considered in the case of odd $n$. Using the equation for the spin connection of general form, it is shown that the problem of the local Pauli's theorem is equivalent to the problem of existence of a solution of some special system of partial differential equations. The special cases $n=2$, $r\geq 1$ and $n\geq 2$, $r=1$ with more simpler solution of the problem are considered in detail.
Pauli's Theorem and Quantum Canonical Pairs: The Consistency Of a Bounded, Self-Adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum
