Quantization, dequantization, and distinguished states

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
Eli Hawkins, Christoph Minz and Kasia Rejzner
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引用次数: 0

Abstract

Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and—using techniques of geometric quantization—construct the quantum algebra and equip it with a distinguished state. We compare our result with the construction due to Sorkin—which starts from the same input data—and show that our distinguished state coincides with the Sorkin-Johnson state. Sorkin’s construction was originally applied to the free scalar field over a causal set (locally finite, partially ordered set). Our perspective suggests a natural generalization to less linear examples, such as an interacting field.
量化、去量化和区分状态
几何量子化是一种从经典数据出发构建量子模型的自然方法。在这项研究中,我们从具有内积的交错向量空间出发,利用几何量子化技术构建量子代数,并为其配备一个区分态。我们将我们的结果与索金的构造(从相同的输入数据出发)进行了比较,结果表明我们的区分态与索金-约翰逊态重合。索金的构造最初应用于因果集(局部有限、部分有序集)上的自由标量场。我们的观点表明,它可以自然地推广到线性程度较低的例子中,例如相互作用场。
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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