Category Archives: Preprints

P.C.M. Flores, D.A.L Pablico and E.A. Galapon, “Instantaneous tunneling time within the theory of time-of-arrival operators,” arXiv:2409.12389

By | September 22, 2024
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It has been shown in \href{this https URL}{\textit{Phys. Rev. Lett.}, \textbf{108} 170402 (2012)}, that quantum tunneling is instantaneous using a time-of-arrival (TOA) operator constructed by Weyl quantization of the classical TOA. However, there are infinitely many possible quantum images of the classical TOA, leaving it unclear if one is uniquely preferred over the others. This… Read More »

N.L.R. Rojas and E.A. Galapon, “Terminating Poincare asymptotic expansion of the Hankel transform of entire exponential type functions,” arXiv:2409.10948

By | September 19, 2024
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We perform an asymptotic evaluation of the Hankel transform, , for arbitrarily large of an entire exponential type function, , of type by shifting the contour of integration in the complex plane. Under the situation that has an odd parity with respect to and the condition that the asymptotic parameter is greater than the type… Read More »

R.J.C. Bagunu and E.A. Galapon, “Quantization of the Hamilton Equations of Motion,” arXiv:2409.03348

By | September 19, 2024
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One of the fundamental problems in quantum mechanics is finding the correct quantum image of a classical observable that would correspond to experimental measurements. We investigate for the appropriate quantization rule that would yield a Hamiltonian that obeys the quantum analogue of Hamilton’s equations of motion, which includes differentiation of operators with respect to another… Read More »

D.A.L. Pablico, J.J.P. Magadan, C.L. Arguelles and E.A. Galapon, “The role of conjugacy in the dynamics of time of arrival operators,” arXiv:2404.16298

By | April 27, 2024
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The role of conjugacy in the dynamics of time of arrival operators The construction of time of arrival (TOA) operators canonically conjugate to the system Hamiltonian entails finding the solution of a specific second-order partial differential equation called the time kernel equation (TKE). An expanded iterative solution of the TKE has been obtained recently in… Read More »

C.D. Tica, P.J. Blancas and E.A. Galapon, “Exact Evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian II: Non-alternating Case,” https://arxiv.org/abs/2402.14839

By | March 9, 2024
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We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant electric field and electric-like self-dual background. We also devise a prescription based on the finite-part integration of the Cauchy principal value integral to sum… Read More »

C.D. Tica and E.A. Galapon, “Exact evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian I: Alternating Case,” https://arxiv.org/abs/2310.08199

By | March 9, 2024
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We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant magnetic field and magnetic-like self-dual background. We also devise a prescription based on the finite-part integration of a generalized Stieltjes integral to sum and… Read More »

C.D. Tica and E.A. Galapon, “Summation and Extrapolation of Divergent Perturbation Series with logarithmic non-pertubative behavior,” https://arxiv.org/abs/2310.08199

By | November 1, 2023
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We devise a prescription based on the finite-part integration of the generalized Stieltjes integral [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to sum the associated divergent series of Stieltjes across all asymptotic regimes. The prescription utilizes the divergent negative-power moments which we treated as Hadamard’s finite part integrals to transform the divergent weak-field perturbation expansions for… Read More »

P.J.D. Blancas and E.A. Galapon, “Finite-part integration of the Hilbert transform,” https://arxiv.org/abs/2210.14462

By | November 1, 2023
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This is a major revision of the original preprint. The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms—the first is an infinite series of finite-part of divergent integrals, and the… Read More »

C.D. Tica and E.A. Galapon, “Continuation of the Stieltjes Series to the Large Regime by Finite-part Integration,” https://arxiv.org/abs/2302.03891

By | March 5, 2023
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A prescription is devised to utilize a novel convergent expansion in the strong-asymptotic regime of the Stieltjes integral and its generalizations [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to sum the associated divergent series of Stieltjes across all asymptotic regimes. The novel expansion makes use of the divergent negative-power moments which were treated as Hadamard’s finite… Read More »

P.J.D. Blancas and E.A. Galapon, “Finite-part integration of the Hilbert transform,” https://arxiv.org/abs/2210.14462

By | October 27, 2022
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Finite-part integration is a recently introduced method of evaluating well-defined integrals using the finite-part of divergent integrals [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. Here finite-part integration is applied in the exact evaluation of the one-sided, , and full, , Hilbert transforms, together with the reductions of the later transform when is a… Read More »