  This study considers the operator $\hat{T}$ corresponding to the classical
spacetime four-volume $\tilde{T}$ (on-shell) of a finite patch of spacetime in
the context of Unimodular Loop Quantum Cosmology for the homogeneous and
isotropic model with flat spatial sections and without matter sources. Since
the spacetime four-volume is canonically conjugate to the cosmological
"constant", the operator $\hat{T}$ is constructed by solving its canonical
commutation relation with $\hat{\Lambda}$ - the operator corresponding to the
classical cosmological constant on-shell $\tilde{\Lambda}$. This conjugacy,
along with the action of $\hat{T}$ on definite volume states reducing to
$\tilde{T}$, allows us to interpret that $\hat{T}$ is indeed a quantum
spacetime four-volume operator. The discrete spectrum of $\hat{T}$ is
calculated by considering the set of all $\tau$'s where the eigenvalue equation
has a solution $\Phi_{\tau}$ in the domain of $\hat{T}$. It turns out that,
upon assigning the maximal domain $D(\hat{T})$ to $\hat{T}$, we have
$\Phi_{\tau}\in D(\hat{T})$ for all $\tau\in\mathbb{C}$ so that the spectrum of
$\hat{T}$ is purely discrete and is the entire complex plane. A family of
operators $\hat{T}^{(b_0,\phi_0)}$ was also considered as possible self-adjoint
versions of $\hat{T}$. They represent the restrictions of $\hat{T}$ on their
respective domains $D(\hat{T}^{(b_0,\phi_0)})$ which are just the maximal
domain with additional quasi-periodic conditions. Their possible
self-adjointness is motivated by their discrete spectra only containing real
and discrete numbers $\tau_m$ for $m=0,\pm1,\pm2,...$.

General Relativity and Quantum Cosmology