因果摄动QFT和白噪声

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-09-06 DOI:10.1142/s0219025723500121

Jaroslaw Wawrzycki

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引用次数: 0

摘要

在本文中，我们提出了Bogoliubov的因果微扰QFT，它只包括一个改进:在一个点上的产生-湮灭算子，即对于一个特定的动量，在数学上被解释为来自白噪声分析的Hida算子。我们保持理论的其余部分完全不变。这允许避免红外和紫外线在过渡到绝热极限的相互作用场的发散。本文用希达算符作为产生-湮灭算符，对散射算符的因果公理进行了分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Causal perturbative QFT and white noise

In this paper, we present the Bogoliubov’s causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared — and ultraviolet — divergences in the transition to the adiabatic limit for interacting fields. We present here the analysis of the causal axioms for the scattering operator with the Hida operators as the creation-annihilation operators.

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来源期刊

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.