arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2402.05795quant-phgr-qchep-th
收藏

Unruh-DeWitt模型及其联合相互作用Hilbert空间

The Unruh-DeWitt model and its joint interacting Hilbert space

Erickson Tjoa, Finnian Gray

备注：
47+7 pages, single-column; 1 figure; v2: fixed typos and updated to match published version
发表信息：
2024 J. Phys. A: Math. Theor. 57 325301
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本研究建立了Unruh-DeWitt粒子探测器模型与spin-boson模型的严格联系，证明了时空涂抹函数可调节紫外行为但仍存在红外发散，并阐明了联合Hilbert空间的构造障碍及算子代数方法的适用性。

摘要：

在这项工作中，我们建立了应用于弯曲时空量子场论的Unruh-DeWitt粒子探测器模型与spin-boson模型严格构造之间的联系。通过一些修改，我们证明了关于spin-boson基态存在性的现有结果可以适用于Unruh-DeWitt模型。在涉及(3+1)维全局双曲时空中无质量标量场的最相关场景中，Unruh-DeWitt模型描述了光与物质相互作用的简化模型，我们论证了时空涂抹函数的常见选择能够调节模型的紫外行为，但仍可能表现出红外发散。特别地，这意味着一个众所周知的预期，即该模型的联合相互作用Hilbert空间无法由二维复Hilbert空间与真空表示的Fock空间的张量积来描述。我们讨论了该问题不会出现的条件，以及算子代数方法对于更好理解粒子探测器模型及其应用的相关性。我们的工作阐明了spin-boson模型中Haag定理导致的障碍与红外玻色子之间的联系，并为在涉及多个探测器的UDW框架中更严格地研究纠缠与通信铺平了道路。

英文摘要：

In this work we make the connection between the Unruh-DeWitt particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson model. With some modifications, we show that existing results about the existence of a spin-boson ground state can be adapted to the Unruh-DeWitt model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the Unruh-DeWitt model describes a simplified model of light-matter interaction, we argue that common choices of the spacetime smearing functions regulate the ultraviolet behaviour of the model but can still exhibit infrared divergences. In particular, this implies the well-known expectation that the joint interacting Hilbert space of the model cannot be described by the tensor product of a two-dimensional complex Hilbert space and the Fock space of the vacuum representation. We discuss the conditions under which this problem does not arise and the relevance of the operator-algebraic approach for better understanding of particle detector models and their applications. Our work clarifies the connection between obstructions due to Haag's theorem and infrared bosons in the spin-boson models, and paves the way for more rigorous study of entanglement and communication in the UDW framework involving multiple detectors.

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。

↑