二次量子化中的玻色子-费米子代数映射。

IF 2.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Entropy Pub Date : 2024-12-08 DOI:10.3390/e26121067

Fabio Lingua, Diego Molina Peñafiel, Lucrezia Ravera, Sebastián Salgado

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引用次数: 0

摘要

我们提出了一种基于产生算子和湮灭算子的玻色子代数映射到费米子代数的代数方法，并引入了玻色子和费米子发生器之间的适当识别。由此得到的代数结构对应于一个变形的grassmann型代数，涉及反交换的grassmann型变量。然后讨论了后者在第二次量化中实现规范不变性所起的作用。本文讨论了映射在玻色子和费米子谐振子哈密顿子情况下的应用。

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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Boson-Fermion Algebraic Mapping in Second Quantization.

We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained corresponds to a deformed Grassmann-type algebra, involving anticommuting Grassmann-type variables. The role played by the latter in implementing gauge invariance in second quantization within our procedure is then discussed. This discussion includes the application of the mapping to the case of the bosonic and fermionic harmonic oscillator Hamiltonians.

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来源期刊

Entropy PHYSICS, MULTIDISCIPLINARY-

CiteScore

4.90

自引率

11.10%

发文量

1580

审稿时长

21.05 days

期刊介绍： Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.