两个实标量场和希格斯玻色子的一般标量势的有界-无界条件

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

Theoretical and Mathematical Physics Pub Date : 2024-09-24 DOI:10.1134/S0040577924090101

Yisheng Song, Liqun Qi

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引用次数: 0

摘要

两个实标量场和一个希格斯玻色子的最一般标量势是三变量的四次同次多项式，它定义了一个（4）阶三维对称张量。因此，这种标量势的有界性涉及相应张量的正（半）定性。因此，本文主要讨论这种特殊张量的正（半）定性的解析表达式。首先，本文给出了检验二维对称张量正（半）定域的解析必要条件和充分条件。此外，通过这一结果，还得到了两个实标量场和希格斯玻色子的一般标量势的自下而上有界性的解析必要条件和充分条件。

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Boundedness-below conditions for a general scalar potential of two real scalar fields and the Higgs boson

The most general scalar potential of two real scalar fields and a Higgs boson is a quartic homogeneous polynomial in three variables, which defines a \(4\)th-order three-dimensional symmetric tensor. Hence, the boundedness of such a scalar potential from below involves the positive (semi-)definiteness of the corresponding tensor. In this paper, we therefore mainly discuss analytic expressions of positive (semi-)definiteness for such a special tensor. First, an analytically necessary and sufficient condition is given to test the positive (semi-)definiteness of a \(4\)th-order two-dimensional symmetric tensor. Furthermore, by means of such a result, the analytic necessary and sufficient conditions of the boundedness from below are obtained for a general scalar potential of two real scalar fields and the Higgs boson.

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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.