LÉVY PROCESSES ON THE LORENTZ-LIE ALGEBRA

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI:10.1142/9789811275999_0003

Ameur Dhahri, Uwe Franz

引用次数: 0

Abstract

Levy processes in the sense of Schurmann on the Lie algebra of the Lorentz grouop are studied. It is known that only one of the irreducible unitary representations of the Lorentz group admits a non-trivial one-cocycle. A Schurmann triple is constructed for this cocycle and the properties of the associated Levy process are investigated. The decommpositions of the restrictions of this triple to the Lie subalgebras $so(3)$ and $so(2,1)$ are described.

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LÉvy洛伦兹-李代数的过程

研究了Lorentz群李代数上Schurmann意义上的Levy过程。已知在洛伦兹群的不可约酉表示中，只有一个存在非平凡的一环。构造了该循环的Schurmann三重体，并研究了相关Levy过程的性质。描述了这个三元组的约束分解为李子代数$so(3)$和$so(2,1)$。

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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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.