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对方箱归一化下的自由实标量场系统的等时对易关系的 一点物理认识与讨论

  • 孙为民
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  • 南京大学物理学院,江苏南京210093
孙为民,( 1973—) ,男,江苏苏州人,南京大学物理学院现代物理系副教授,博士,主要从事量子规范

网络出版日期: 2017-01-20

基金资助

江苏省自然科学基金项目( BK20151376) 资助

Physical cognition and discussion on the equal time commutation relation of a free real scalar field system under box normalization

  • SUN Wei-min
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  • School of Physics,Nanjing University,Nanjing,Jiangsu 210093,China

Online published: 2017-01-20

摘要

讨论了在方箱归一化之下的自由实标量场系统的等时对易关系,发现根据通常自由场理论的粒子解释出发,自由实标量场系统的等时对易关系,在自然数学的意义上,应该是以某一个周期性延拓形式的狄拉克δ - 函数来代替通常的狄拉克δ - 函数,这一点在数学上看,既是自然的,也是必然的,而在无穷体积极限之下,自由实标量场的等时对易关系可以自然的 回复至标准的原有形式. 本文中对于这一事实作了详细的讨论与论证,并且从物理的角度,对于场论中方箱归一化处理之物   理实质内涵,作出了一定的探讨性的分析,给出了一点基本的认识.

本文引用格式

孙为民 . 对方箱归一化下的自由实标量场系统的等时对易关系的 一点物理认识与讨论[J]. 大学物理, 2017 , 36(1) : 4 -7 . DOI: 10. 16854 /j. cnki. 1000-0712. 2017. 01. 002

Abstract

The equal - time commutation relation of a free real scalar field system under box normalization is discussed. It is found that according to the usual particle interpretation of a free field theory, the equal - time commutation relation of a free real scalar field system, in the sense of natural mathematics,should use some periodically continued Dirac delta function to replace the usual Dirac delta function. Mathematically,this is both natural and necessary,and the equal - time commutation relation of a free real scalar field could naturally revert to the original standard form in the infinite volume limit. This paper gives detailed discussion and demonstration for this fact,and from the angle of physics makes some speculative analysis for the physical essence of the box normalization treatment in field theory,as well as gives some fundamental cognition.
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