玻色子Fock空间的Berezin和Smolyanov表示之间的显式bargmann型同构

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2025-04-25 DOI:10.1134/S0040577925040105

N. N. Shamarov, M. V. Shamolin

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引用次数: 0

摘要

对于具有对合的无限维空间\(H\)，我们构造了一个由Fock空间\(\Gamma(H)\)的单粒子部分\(H\)定义的bargmann型同构。所得公式在\(\dim H<\infty\)情况下也有意义，并且与Segal-Bargmann空间密切相关。构造的核心是在测试函数的无限维域中移位不变分布的概念。

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Explicit Bargmann-type isomorphism between Berezin and Smolyanov representations of bosonic Fock spaces

We construct a Bargmann-type isomorphism defined by the one-particle part \(H\) of the Fock space \(\Gamma(H)\) for an infinite-dimensional space \(H\) with involution. The formulas obtained also make sense in the case \(\dim H<\infty\) and are closely related to the Segal–Bargmann space. Central to the construction is the notion of a shift-invariant distribution in the case of an infinite-dimensional domain of test functions.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.