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Publications (5)
As a follow-up to a recent study in the spin-0 case [J. Bunao and E. A.
Galapon, Ann. Phys. 353, 83-106 (2015)], we construct a one-particle Time of
Arrival (TOA) operator conjugate to a Hamiltonian describing a free
relativistic spin-1/2 particle in one spatial dimension. Upon transformation in
a representation where the Hamiltonian is diagonal, i...
We construct a one-particle TOA operator $\mathcal{\hat{T}}$ canonically
conjugate with the Hamiltonian describing a free, charged, spin-$0$,
relativistic particle in one spatial dimension and show that it is maximally
symmetric. We solve for its eigenfunctions and show that they form a complete
and non-orthogonal set. Plotting the time evolution o...
The Bender-Dunne basis operators, $\mathsf{T}_{-m,n}=2^{-n}\sum_{k=0}^n {n
\choose k} \mathsf{q}^k \mathsf{p}^{-m} \mathsf{q}^{n-k}$ where $\mathsf{q}$
and $\mathsf{p}$ are the position and momentum operators respectively, are
formal integral operators in position representation in the entire real line
$\mathbb{R}$ for positive integers $n$ and $m$...
This study considers the operator T corresponding to the classical spacetime four-volume 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 fourvolume is canonically conjugate to the cosmolo...
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