关键词: 自由实标量场, 等时对易关系, 方箱归一化

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.

Key words: free real scalar field, equal time commutation relation, box normalization