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 »

D.A.L. Pablico and E.A. Galapon, “Moyal deformation of the classical time of arrival,” https://arxiv.org/abs/2309.00222

By | November 1, 2023
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The quantum time of arrival (TOA) problem requires statistics of the measured arrival times given only the initial state of a particle. Following the standard framework of quantum theory, the problem translates into finding an appropriate quantum image of the classical arrival time , usually in operator form . In this paper, we consider 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 »

P.C.M. Flores and E.A. Galapon, “Instantaneous tunneling of relativistic massive spin-0 particles,” https://arxiv.org/abs/2207.09040

By | July 20, 2022
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The tunneling time problem earlier studied in \href{https://link.aps.org/doi/10.1103/PhysRevLett.108.170402}{Phys. Rev. Lett. \textbf{108}, 170402 (2012)} using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous implying that the wavepacket becomes superluminal below the barrier. The non-relativistic treatment raises the question whether the superluminal behavior is a mere non-relativistic phenomenon or an an inherent quantum effect… Read More »

D.A.L. Pablico and E.A. Galapon, “Quantum corrections to the Weyl quantization of the classical time of arrival,” https://arxiv.org/abs/2205.08694

By | May 19, 2022
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A time of arrival (TOA) operator that is conjugate with the system Hamiltonian was constructed by Galapon without canonical quantization in [J. Math. Phys. \textbf{45}, 3180 (2004)]. The constructed operator was expressed as an infinite series but only the leading term was investigated which was shown to be equal to the Weyl-quantized TOA-operator for entire… Read More »

E.A. Galapon, “Finite-part integral representation of the Riemann zeta function at odd positive integers and consequent representations,” https://arxiv.org/abs/2203.11342

By | March 23, 2022
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The values of the Riemann zeta function at odd positive integers, , are shown to admit a representation proportional to the finite-part of the divergent integral . Integral representations for are then deduced from the finite-part integral representation. Certain relations between and are likewise deduced, from which integral representations for are obtained.