arXiv subjects

Joseph Bunao

Publications and source records attributed to Joseph Bunao.

5 recordsLinked to original sources

arXiv2024

Generative Flow Networks in Covariant Loop Quantum Gravity

Spin foams arose as the covariant (path integral) formulation of quantum gravity depicting transition amplitudes between different quantum geometry states. As such, they provide a scheme to study the no boundary proposal, specifically the nothing to something transition and compute relevant observables using high performance computing (HPC). Following recent advances, where stochastic algorithms (Markov Chain Monte Carlo-MCMC) were used, we employ Generative Flow Networks, a newly developed machine learning algorithm to compute the expectation value of the dihedral angle for a 4-simplex and compare the results with previous works.

gr-qc↗

arXiv2016

Spacetime Quanta? : The Discrete Spectrum of a Quantum Spacetime Four-Volume Operator in Unimodular Loop Quantum Cosmology

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 $\hatΛ$ - the operator corresponding to the classical cosmological constant on-shell $\tildeΛ$. 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 $τ$'s where the eigenvalue equation has a solution $Φ_τ$ in the domain of $\hat{T}$. It turns out that, upon assigning the maximal domain $D(\hat{T})$ to $\hat{T}$, we have $Φ_τ\in D(\hat{T})$ for all $τ\in\mathbb{C}$ so that the spectrum of $\hat{T}$ is purely discrete and is the entire complex plane. A family of operators $\hat{T}^{(b_0,ϕ_0)}$ was also considered as possible self-adjoint versions of $\hat{T}$. They represent the restrictions of $\hat{T}$ on their respective domains $D(\hat{T}^{(b_0,ϕ_0)})$ 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 $τ_m$ for $m=0,\pm1,\pm2,...$.

gr-qc↗

arXiv2015

A one-particle time of arrival operator for a free relativistic spin-0 charged particle in (1+1) dimensions

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 of their corresponding probability densities, it implies that the eigenfunctions become more localized at the origin at the time equal to their eigenvalues. That is, a particle being described by an eigenfunction of $\mathcal{\hat{T}}$ is in a state of definite arrival time at the origin and at the corresponding eigenvalue. We also calculate the TOA probability distribution of a particle in some initial state.

quant-ph↗

arXiv2015

A Relativistic One-Particle Time of Arrival Operator for a Free Spin-1/2 Particle in (1 + 1) Dimensions

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, it turns out that the constructed operator consists of an operator term $\mathcal{\hat{T}}$ whose action is the same as in the spin-0 case, and another operator term $\mathcal{\hat{T}}_0$ which commutes with the Hamiltonian but breaks invariance under parity inversion. If we must impose this symmetry on our TOA operator, then we can throw away $\mathcal{\hat{T}}_0$ so that the TOA operator is just $\mathcal{\hat{T}}$.

quant-ph↗

arXiv2015

The Bender-Dunne basis operators as Hilbert space operators

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 $m$. We show, by explicit construction of a dense domain, that the operators $\mathsf{T}_{-m,n}$'s are densely defined operators in the Hilbert space $L^2(\mathbb{R})$.

math-ph↗