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

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

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.

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.