当前位置: X-MOL 学术Rev. Math. Phys. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The algebra of Wick polynomials of a scalar field on a Riemannian manifold
Reviews in Mathematical Physics ( IF 1.4 ) Pub Date : 2020-01-30 , DOI: 10.1142/s0129055x20500233
Claudio Dappiaggi 1, 2, 3 , Nicolò Drago 4, 5 , Paolo Rinaldi 1, 2, 3
Affiliation  

On a connected, oriented, smooth Riemannian manifold without boundary we consider a real scalar field whose dynamics is ruled by [Formula: see text], a second-order elliptic partial differential operator of Laplace type. Using the functional formalism and working within the framework of algebraic quantum field theory and of the principle of general local covariance, first we construct the algebra of locally covariant observables in terms of equivariant sections of a bundle of smooth, regular polynomial functionals over the affine space of the parametrices associated to [Formula: see text]. Subsequently, adapting to the case in hand a strategy first introduced by Hollands and Wald in a Lorentzian setting, we prove the existence of Wick powers of the underlying field, extending the procedure to smooth, local and polynomial functionals and discussing in the process the regularization ambiguities of such procedure. Subsequently we endow the space of Wick powers with an algebra structure, dubbed E-product, which plays in a Riemannian setting the same role of the time-ordered product for field theories on globally hyperbolic spacetimes. In particular, we prove the existence of the E-product and we discuss both its properties and the renormalization ambiguities in the underlying procedure. As the last step, we extend the whole analysis to observables admitting derivatives of the field configurations and we discuss the quantum Møller operator which is used to investigate interacting models at a perturbative level.

中文翻译:

黎曼流形上标量场的 Wick 多项式的代数

在一个连通的、有向的、光滑的无边界黎曼流形上,我们考虑一个实数标量场,其动力学由拉普拉斯型的二阶椭圆偏微分算子 [公式:见正文] 支配。使用泛函形式主义并在代数量子场论和一般局部协方差原理的框架内工作,首先我们根据仿射空间上的一束光滑正则多项式泛函的等变截面构造局部协变可观测量的代数与[公式:见文本]相关的参数。随后,采用由 Hollands 和 Wald 在洛伦兹环境中首次引入的策略,我们证明了潜在场的 Wick 幂的存在,将过程扩展为平滑,局部和多项式泛函,并在此过程中讨论此类过程的正则化模糊性。随后,我们赋予 Wick 幂空间一个代数结构,称为 E 积,它在黎曼设置中起着与全局双曲时空场论的时间序积相同的作用。特别是,我们证明了 E 积的存在,并讨论了它的性质和基础过程中的重整化模糊性。作为最后一步,我们将整个分析扩展到承认场配置导数的可观测量,并讨论用于研究微扰水平相互作用模型的量子 Møller 算子。被称为 E 乘积,它在黎曼设置中扮演与全球双曲时空场论的时间序乘积相同的角色。特别是,我们证明了 E 积的存在,并讨论了它的性质和基础过程中的重整化模糊性。作为最后一步,我们将整个分析扩展到承认场配置导数的可观测量,并讨论用于研究微扰水平相互作用模型的量子 Møller 算子。被称为 E 乘积,它在黎曼设置中扮演与全球双曲时空场论的时间序乘积相同的角色。特别是,我们证明了 E 积的存在,并讨论了它的性质和基础过程中的重整化模糊性。作为最后一步,我们将整个分析扩展到承认场配置导数的可观测量,并讨论用于研究微扰水平相互作用模型的量子 Møller 算子。
更新日期:2020-01-30
down
wechat
bug