Complete Set of Unitary Irreps of Discrete Heisenberg Group \( HW_{2^{s}}\)

IF 1.3 4区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY International Journal of Theoretical Physics Pub Date : 2025-01-18 DOI:10.1007/s10773-025-05888-9

E. Floratos, I. Tsohantjis

引用次数: 0

Abstract

Following the method of induced group representations of Wigner-Mackay, the explicit construction of all the unitary irreducible representations of the discrete finite Heisenberg-Weyl group \(HW_{2^{s}}\) over the discrete phase space lattice \(\mathbb {Z}_{2^{s}}\otimes \) \(\mathbb {Z}_{2^{s}}\) is presented. We explicitly determine their characters and their fusion rules. We discuss possible physical applications for finite quantum mechanics and quantum computation.

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离散Heisenberg群的酉逆的完备集 \( HW_{2^{s}}\)

根据Wigner-Mackay的诱导群表示方法，给出了离散相空间晶格\(\mathbb {Z}_{2^{s}}\otimes \)\(\mathbb {Z}_{2^{s}}\)上离散有限Heisenberg-Weyl群\(HW_{2^{s}}\)的所有幺正不可约表示的显式构造。我们明确地确定了它们的特征和它们的融合规则。我们讨论了有限量子力学和量子计算可能的物理应用。

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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来源期刊

International Journal of Theoretical Physics 物理-物理：综合

CiteScore

2.50

自引率

21.40%

发文量

258

审稿时长

3.3 months

期刊介绍： International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.

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