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非线性规范变换的结构

Structure of nonlinear gauge transformations

Marek Czachor

备注：
Final version, to be published in Phys.Rev.A (Rapid Communication), April 1998
发表信息：
Phys.Rev. A57 (1998) 2263
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摘要：

用波函数$ψ(x)$定义的非线性Doebner-Goldin [Phys.Rev.A54，3764（1996）]规范变换（NGT）不形成群。为了得到一个群的性质，必须考虑在复变元函数的不同分支上作用不同的变换，并且对于定义良好的NGT来说，$ψ(x)$的值的知识是不够的。根据$ψ(x)$良好定义的NGT形成由实数$γ$和非零$λ$参数化的半群，所述非零$λ$是整数或$-1\leq λ\leq 1$。将NGT扩展到投影仪和一般密度矩阵，得到具有复数$γ$的NGT。密度矩阵演化的线性性和厄米性都是与规范有关的性质。

英文摘要：

Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations (NGT) defined in terms of a wave function $ψ(x)$ do not form a group. To get a group property one has to consider transformations that act differently on different branches of the complex argument function and the knowledge of the value of $ψ(x)$ is not sufficient for a well defined NGT. NGT that are well defined in terms of $ψ(x)$ form a semigroup parametrized by a real number $γ$ and a nonzero $λ$ which is either an integer or $-1\leq λ\leq 1$. An extension of NGT to projectors and general density matrices leads to NGT with complex $γ$. Both linearity of evolution and Hermiticity of density matrices are gauge dependent properties.

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