We carry out the canonical analysis of a covariant version of unimodular gravity in terms of the connection representation. We then proceed to quantize this theory by implementing the Dirac procedure. We confirm whether and how the Kodama state, which is a solution of quantum general relativity, can be extended into covariant unimodular gravity. Finally, we discuss the difference of quantum states between covariant unimodular gravity, the original unimodular gravity, and general relativity.

中文翻译：

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协变单模引力的规范分析和 Kodama 状态的扩展

我们根据连接表示对协变版本的单模引力进行规范分析。然后我们通过实施狄拉克程序来量化这个理论。我们确认了作为量子广义相对论的解的 Kodama 状态是否以及如何可以扩展到协变单模引力。最后，我们讨论了协变单模引力、原始单模引力和广义相对论之间的量子态差异。