带量子位相的谐振子及其表示

ON THE HARMONIC OSCILLATOR WITH QUANTUM PHASE AND ITS REPRESENTATION

说明带量子位相的谐振子可以为场的量子化提供一条新的途径,重点研究这种谐振子的数学特性,即它的表示理论.讨论它的Fock空间表示(它是有限维的)和相干态表示,定义了统计学特性完全不同的两类相干态.

The paper first shows that the harmonic oscillator with quantum phase may provide a new way for quantization of field, then mainly studies the mathematicl characteristics of the harmonic oscillator with quantum phase, i.e., its representation theory. The representation in Fock space (being finite-dimensional) and two kinds of coherent states are discussed. It is shown that the statistical properties of the two kinds of coherent states are entirely different.