量子色动力学中Schwinger-Dyson方程解的适定性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (1): 234-242.

量子色动力学中Schwinger-Dyson方程解的适定性

胡凤¹(),张瑞凤^2,*()

¹ 河南大学国际教育学院河南开封 475001
² 河南大学数学与统计学院河南开封 475004

收稿日期:2018-06-07 出版日期:2020-02-26 发布日期:2020-04-08
通讯作者: 张瑞凤 E-mail:hedahufeng@126.com;zrf615@henu.edu.cn
作者简介:胡凤, E-mail:hedahufeng@126.com
基金资助:
国家自然科学基金(11471099);国家自然科学基金(11671120)

Well-Posedness of the Solution of Schwinger-Dyson Equation in Quantum Chromodynamics

Feng Hu¹(),Ruifeng Zhang^2,*()

¹ International Education College, Henan University, Henan Kaifeng 475001
² College of Mathematics and Statistics, Henan University, Henan Kaifeng 475004

Received:2018-06-07 Online:2020-02-26 Published:2020-04-08
Contact: Ruifeng Zhang E-mail:hedahufeng@126.com;zrf615@henu.edu.cn
Supported by:
国家自然科学基金(11471099);国家自然科学基金(11671120)

摘要/Abstract

摘要：

该文研究了在有限温度下量子色动力学中一类Schwinger-Dyson积分方程问题，利用积分方程理论和泛函分析，得到了积分方程解的适定性.进一步，该文证明了手征对称性破缺、保持在量子色动力学中状态转变的临界温度T_c的存在唯一性.

关键词: 量子色动力学, Schwinger-Dyson方程, 上下解方法

Abstract:

In this paper, we study the Schwinger-Dyson integral equation in quantum chromodynamics under the condition of the finite-temperature. Applying the theory of integral equation and functional analysis, we get the well-posedness of the solution of Schwinger-Dyson integral equation. Furthermore, we prove the existence and uniqueness of critical temperature T_c, which separates the low-temperature phase where the chiral symmetry is spontaneously broken from the high-temperature phase where the chiral symmetry restores in quantum chromodynamics.

Key words: Quantum chromodynamics, Schwinger-Dyson equations, Sub and super solution method

中图分类号:

O175.2

胡凤,张瑞凤. 量子色动力学中Schwinger-Dyson方程解的适定性[J]. 数学物理学报, 2020, 40(1): 234-242.

Feng Hu,Ruifeng Zhang. Well-Posedness of the Solution of Schwinger-Dyson Equation in Quantum Chromodynamics[J]. Acta mathematica scientia,Series A, 2020, 40(1): 234-242.

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