Local Generalized Pauli's Theorem

Details Local Generalized Pauli's Theorem Local Generalized Pauli's Theorem

2012-01-24

arxiv.org/abs/1201.4985v1

Physics

Mathematical Physics

6 pages

Scientific paper

In this work a generalized Pauli's theorem (proved by D. S. Shirokov for two sets $e^a, h^a$, $a=1,...,n$ of Clifford algebra elements $Cl(p,q)$, $p+q=n$) is extended to the case, when one or both sets of elements depends smoothly on points $x$ of the Euclidian space. We prove that in this case for any point $x_0$ of Euclidian space there exists $\epsilon$-neighborhood $O_\epsilon(x_0)$ and there exists smooth function $T : O_\epsilon(x_0)\to Cl(p,q)$ such that two sets of Clifford algebra elements are connected by a similarity transformation $h^a(x)=T(x)^{-1}e^a(x)T(x)$, $a=1,...,n$ in $O_\epsilon(x_0)$.

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