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

Canonical analysis of covariant unimodular gravity and an extension of the Kodama state