具有Hopf项的$CP^{1}$模型的De Rham上同调
De Rham Cohomology of $CP^{1}$ model with Hopf term
摘要：
本文研究了具有Hopf项的$CP^{1}$模型，该模型满足第二类约束，并允许定义良好的BRST算子$Q$ .利用算子$Q$，通过所有$Q$ -闭和$Q$ -正合鬼数$p$ -形式的集合导出相应的商群，显式地构造了它的de Rham上同调群.此外，我们研究了不含Hopf项的$CP^{1}$模型，以评估Hopf项对上同调群的影响。我们发现，Hopf项的de Rham上同调的影响源自希尔伯特空间修改这个Hopf项。
英文摘要：
We investigate the $CP^{1}$ model possessing the Hopf term which respects the second class constraints and admits the well defined the BRST operator $Q$. Using the operator $Q$, we explicitly construct its de Rham cohomology group by deriving the ensuing quotient group via both the collections of all $Q$-closed and $Q$-exact ghost number $p$-forms. Moreover, we study the $CP^{1}$ model without the Hopf term to evaluate the ensuing effect of the Hopf term on the cohomology group. We find that the Hopf term effects on the de Rham cohomology originate from the Hilbert space modified by this Hopf term.
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