自由电磁场理论的量子规范变换和生成元判据

Quantum gauge transformation in free electromagnetic field theory and its generator criterion

研究了自由电磁场理论中从库伦规范到一类较广泛的静态规范的量子规范变换,得到了静态规范中的形式场论结构,包括对易关系、运动方程、Poincaré变换生成元,并检验了由核子自旋结构问题所提出的规范场理论动量和角动量算符分解的生成元判据,丰富和充实了相关研究结果。

The implementation of quantum gauge transformation in gauge theories is a long-standing and unsolved problem in quantum field theory. A formal language and framework for such a description have been established by Strocchi and Wightman in the 1970 s, but no explicit construction of such a connection exists for nontrivial cases. This is even the case for the free electromagnetic field theory. In my work, an attempt is given to seek an explicit realization of quantum gauge transformation from Coulomb gauge to a class of static gauges in free electromagnetism. By means of a general map between Coulomb gauge variable and the static gauge variable on the same Hilbert space, such a quantum gauge transformation is firmly established in a true mathematical sense. The formal field-theoretic structure of the free electromagnetic field theory in the static gauge has been obtained, including the commutation relations, the equation of motion and the construction of Poincaré generators. As an application of this new formalism, the so-called 'generator criterion' for the decomposition of momentum and angular momentum operators in gauge theories, which has been posed in the study of nucleon spin structure, is explicitly checked, with some physically interesting results obtained.This construction can in principle be generalized to the case of the interacting theory of photons and charged particles,which will be undertaken in the future.