arXivDaily arXiv每日学术速递 周一至周五更新
arXiv quant-ph/0002013quant-ph
收藏

量子理论中的非线性透视

Perspectives on Nonlinearity in Quantum Theory

Gerald A. Goldin

摘要:

以一般线性群GL(2,R)为模型的扩大的非线性变换群G,在波函数的相位和其振幅的对数之间产生了一种美丽的、显然未被注意到的对称性。多布纳和我之前提出的方程被嵌入到一个更广泛的、自然的非线性时间演化方程族中,G在这个方程族中充当规范群(使物理观测保持不变)。在特定的规范下,存在G不变量,它们可以简化为可线性化的量子理论通常的概率密度和通量。

英文摘要:

An enlarged group G of nonlinear transformations, modeled on the general linear group GL(2,R), leads to a beautiful, apparently unremarked symmetry between the wave function's phase and the logarithm of its amplitude. Equations Doebner and I earlier proposed are embedded in a wider, natural family of nonlinear time-evolution equations, on which G acts as a gauge group (leaving physical observations invariant). There exist G-invariant quantities that reduce to the usual probability density and flux for linearizable quantum theories in a particular gauge.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑