论文标题
相互作用的一维量子系统中的通用二元转换
Universal duality transformations in interacting one-dimensional quantum systems
论文作者
论文摘要
一维量子系统允许双重关系，通过Girardeau的映射定理将硬核无旋转玻色子和费米子置于一对一的信件中。通过零范围相互作用的软玻色子的最简单模型也可以映射到双重相互作用的费米子上。但是，在无旋转，稀疏或多组分情况下，一种对任意低能相互作用的一维统计转移的系统方法仍然难以捉摸。我开发了一种一般的理论，即具有任意自旋或内部结构的玻色子和费米子的一维量子系统，单粒子分散体（包括非偏见，相对论或其他方式）以及普遍状态中低能的相互作用。这些转变产生了新的二元关系和模型的家庭，这些家族与各个双重理论的强大和弱耦合限制相关联。
One-dimensional quantum systems admit duality relations that put hard core spinless bosons and fermions in one-to-one correspondence via Girardeau's mapping theorem. The simplest models of soft bosons interacting via zero-range potentials can also be mapped onto dual interacting fermions. However, a systematic approach to one-dimensional statistical transmutation for arbitrary low-energy interactions in the spinless and spinful or multicomponent cases has remained elusive. I develop a general theory of local unitary transformations between one-dimensional quantum systems of bosons and fermions with arbitrary spin or internal structure, single-particle dispersion -- including non-relativistic, relativistic or otherwise -- and low-energy interactions in the universal regime. These transformations generate families of new duality relations and models that relate the strong and weak coupling limits of the respective dual theories.
