论文标题
圆柱体的经典和量化的分解代数
Classical and quantised resolvent algebras for the cylinder
论文作者
论文摘要
Buchholz and Grundling（Comm。Math。Phys。，272，699--750，2007）引入了C $^\ ast $ -Algebra，称为分解代数，作为对符号矢量空间的规范量化，并证明了该代数具有多个值得的功能。我们通过首先概括了本文第一批作者定义的分辨率代数的经典类似物，在$ n $ torus的$ n $ torus上定义了它们的分解代数的类似物$ t^*\ mathbb {t}^n $，该$ n $ torus的经典类似物（J. Function。Anal.277，277，277，2815-2815-2838，2015-2838，2015-2838，和2019年）。我们证明，从瑞夫（Rieffel）的意义上讲，这种量化几乎是严格的，并表明我们的分解代数与原始分解代数具有许多功能。我们证明，我们的经典和量化代数都在与大型电位相对应的时间演变下封闭。最后，我们讨论了它们与晶格仪理论的相关性。
Buchholz and Grundling (Comm. Math. Phys., 272, 699--750, 2007) introduced a C$^\ast$-algebra called the resolvent algebra as a canonical quantisation of a symplectic vector space, and demonstrated that this algebra has several desirable features. We define an analogue of their resolvent algebra on the cotangent bundle $T^*\mathbb{T}^n$ of an $n$-torus by first generalizing the classical analogue of the resolvent algebra defined by the first author of this paper in earlier work (J. Funct. Anal., 277, 2815--2838, 2019), and subsequently applying Weyl quantisation. We prove that this quantisation is almost strict in the sense of Rieffel and show that our resolvent algebra shares many features with the original resolvent algebra. We demonstrate that both our classical and quantised algebras are closed under the time evolutions corresponding to large classes of potentials. Finally, we discuss their relevance to lattice gauge theory.
