arXiv subjects

Jonathan M. M. Hall

Publications and source records attributed to Jonathan M. M. Hall.

15 recordsLinked to original sources

arXiv2026

A Projective Algebra for Ansatz: Resolving Wigner's Puzzle and the Existence of External Realms

Natural philosophy integrates scientific observation with abstract frameworks, often using a mathematical Ansatz to hypothesise about physical phenomena. Exploring the possibility of other universes, however, challenges assumptions that physical laws, like spacetime geometry, extend beyond our reality. This paper argues that mathematical abstractions, serving as a telescope beyond physical constraints, enable such reasoning. Through a projective algebra formalism (Section 4), we model the mechanism of Ansatz, abstractly describing physical objects. This yields a resolution to Wigner's unreasonable effectiveness via cardinality equivalence (Section 5) and clarifies terms like 'evidence' and 'existence' (Section 6) to align with the conventions used in physics. A Cantor-inspired paradox shows no universe can contain all mathematical abstractions (e.g., sets, numbers), as its power set exceeds it, necessitating an external abstract realm (Section 6.4). This logical necessity, which holds even in the context of alternative set theories like New Foundations, provides evidence for a minimal external universe as an abstract realm, supporting Mathematical Realism. This result is not specific to the formalism, as long as we accept that the principles of set theory are mathematically valid. As abstract entities elude empirical detection, logical evidence is apt, guiding future science and philosophy research and fostering interdisciplinary inquiry.

physics.hist-ph↗

arXiv2018

Biological Cell Resonators

This thesis develops the theory of whispering gallery modes, exploring under what conditions a micro or nanoscale device can sustain these resonances, and for which physical criteria the resonance conditions deteriorate. The study is then extended to consider the biological cell in which modes are definitively sustained without artificial assistance. The properties of resonators and their emitted energy spectra are studied within the general framework of the Finite Difference Time Domain method, requiring supercomputing resources to probe the transient behaviour and interactions among the electromagnetic fields. The formal theory of Mie scattering is also extended to develop a cutting-edge, computationally efficient model for general, multilayer microspheres, which represents a valuable achievement for the scientific community in its own right. The model unifies the approaches in the field of mathematical modelling to express the energy spectrum in a single encompassing equation, which is then applied in a range of contexts. The gulf between modelling and biological resonators is bridged by an in-depth study of the physical characteristics of a range of biological cells, and the selection criteria for viable resonator candidates are developed through a number of detailed feasibility studies. The bovine embryo is consequently selected as the optimal choice for this investigation. Evidence is established for the ability of a bovine embryo to sustain whispering gallery modes. The ability of a cell to sustain modes on its own represents a conceptually elegant paradigm for new technologies involving on-site cell interrogation and reporting of the status and health of a biological cell in the future. The methodological and technological developments contained herein thus become a vital asset for the future realisation of autonomous biological cell sensors.

physics.optics↗

arXiv2018

Nucleon Excited States from Lattice QCD and Hamiltonian Effective Field Theory

An approach for relating the nucleon excited states extracted from lattice QCD and the nucleon resonances of experimental data has been developed using the Hamiltonian effective field theory (HEFT) method. By formulating HEFT in the finite volume of the lattice, the eigenstates of the Hamiltonian model can be related to the energy eigenstates observed in Lattice simulations. By taking the infinite-volume limit of HEFT, information from the lattice is linked to experiment. The approach opens a new window for the study of experimentally-observed resonances from the first principles of lattice QCD calculations. With the Hamiltonian approach, one not only describes the spectra of lattice-QCD eigenstates through the eigenvalues of the finite-volume Hamiltonian matrix, but one also learns the composition of the lattice-QCD eigenstates via the eigenvectors of the Hamiltonian matrix. One learns the composition of the states in terms of the meson-baryon basis states considered in formulating the effective field theory. One also learns the composition of the resonances observed in Nature. In this paper, we will focus on recent breakthroughs in our understanding of the structure of the $N^*(1535)$, $N^*(1440)$ and $Λ^*(1405)$ resonances using this method.

nucl-th↗

arXiv2017

The Light-Quark Magnetic Moment of the Lambda(1405) Antikaon-Nucleon Molecule

The light-quark sector of the Lambda(1405) baryon is examined in the context of the recent discovery of a dominant antikaon-nucleon composition at low quark masses. Further evidence for this interpretation of the Lambda(1405) is presented, by calculating the u and d quark contributions to the Lambda(1405) magnetic form factors in lattice QCD. The extent to which these quantities are consistent with the exotic molecular description can then be quantified by comparing the results with the equivalent nucleon form factors. Drawing on a recent extension of the graded-symmetry approach for the flavor-singlet components of the Lambda(1405), the separation of the connected and disconnected contributions is performed in both the flavor-octet and singlet representations. In both cases, the disconnected loop contributions are found to be unexpectedly large. The relationship between the light-quark contributions to the Lambda(1405) magnetic form factor and the connected contributions of the nucleon magnetic form factors is thus confirmed in the case of lattice QCD, establishing compelling evidence for a KN molecular structure of the Lambda(1405) near the physical point.

hep-lat↗

arXiv2017

Study of Low-Lying Baryons with Hamiltonian Effective Field Theory

Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations. We have studied the low-lying baryons $N^*(1535)$, $N^*(1440)$, and $Λ(1405)$. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained at finite volume is excellent. These lattice results also admit a more conventional analysis where the low-energy coefficients are constrained by lattice QCD results, enabling a determination of resonance properties from lattice QCD itself. The role and importance of various components of the Hamiltonian model are examined in the finite volume. The analysis of the lattice QCD data can help us to undertand the structure of these states better.

nucl-th↗

arXiv2017

Structure of the $\mathbf{Λ(1405)}$ from Hamiltonian effective field theory

The pole structure of the $Λ(1405)$ is examined by fitting the couplings of an underlying Hamiltonian effective field theory to cross sections of $K^- p$ scattering in the infinite-volume limit. Finite-volume spectra are then obtained from the theory, and compared to lattice QCD results for the mass of the $Λ(1405)$. Momentum-dependent, non-separable potentials motivated by the well-known Weinberg-Tomozawa terms are used, with SU(3) flavour symmetry broken in the couplings and masses. In addition, we examine the effect on the behaviour of the spectra from the inclusion of a bare triquark-like isospin-zero basis state. It is found that the cross sections are consistent with the experimental data with two complex poles for the $Λ(1405)$, regardless of whether a bare baryon basis state is introduced or not. However, it is apparent that the bare baryon is important for describing the results of lattice QCD at high pion masses.

nucl-th↗

arXiv2016

Light-quark contributions to the magnetic form factor of the Lambda(1405)

In a recent study of the Lambda(1405), the suppression of the strange-quark contribution to the magnetic form factor was interpreted as the discovery of a dominant antikaon-nucleon composition for this low-lying state. We confirm this result by calculating the light u- and d-quark contributions to the Lambda(1405) magnetic form factor in lattice QCD in order to determine the extent to which their contributions support this exotic molecular description. Drawing on the recent graded-symmetry approach for the flavor-singlet components of the Lambda(1405), the separation of connected and disconnected contributions is performed in both the flavor-octet and singlet representations. The relationship between light-quark contributions to the Lambda(1405) magnetic form factor and the connected contributions of the nucleon magnetic form factors is established and compared with lattice calculations of the same quantities, confirming the KN molecular structure of the Lambda(1405) in lattice QCD.

hep-lat↗

arXiv2015

Lattice QCD Evidence that the Lambda(1405) Resonance is an Antikaon-Nucleon Molecule

For almost 50 years the structure of the Lambda(1405) resonance has been a mystery. Even though it contains a heavy strange quark and has odd parity, its mass is lower than any other excited spin-1/2 baryon. Dalitz and co-workers speculated that it might be a molecular state of an antikaon bound to a nucleon. However, a standard quark-model structure is also admissible. Although the intervening years have seen considerable effort, there has been no convincing resolution. Here we present a new lattice QCD simulation showing that the strange magnetic form factor of the Lambda(1405) vanishes, signaling the formation of an antikaon-nucleon molecule. Together with a Hamiltonian effective-field-theory model analysis of the lattice QCD energy levels, this strongly suggests that the structure is dominated by a bound antikaon-nucleon component. This result clarifies that not all states occurring in nature can be described within a simple quark model framework and points to the existence of exotic molecular meson-nucleon bound states.

hep-lat↗

arXiv2015

Method for predicting whispering gallery mode spectra of spherical microresonators

A full three-dimensional Finite-Difference Time-Domain (FDTD)-based toolkit is developed to simulate the whispering gallery modes of a microsphere in the vicinity of a dipole source. This provides a guide for experiments that rely on efficient coupling to the modes of microspheres. The resultant spectra are compared to those of analytic models used in the field. In contrast to the analytic models, the FDTD method is able to collect flux from a variety of possible collection regions, such as a disk-shaped region. The customizability of the technique allows one to consider a variety of mode excitation scenarios, which are particularly useful for investigating novel properties of optical resonators, and are valuable in assessing the viability of a resonator for biosensing.

physics.optics↗

arXiv2015

Predicting the whispering gallery mode spectra of microresonators

The whispering gallery modes (WGMs) of optical resonators have prompted intensive research efforts due to their usefulness in the field of biological sensing, and their employment in nonlinear optics. While much information is available in the literature on numerical modeling of WGMs in microspheres, it remains a challenging task to be able to predict the emitted spectra of spherical microresonators. Here, we establish a customizable Finite- Difference Time-Domain (FDTD)-based approach to investigate the WGM spectrum of microspheres. The simulations are carried out in the vicinity of a dipole source rather than a typical plane-wave beam excitation, thus providing an effective analogue of the fluorescent dye or nanoparticle coatings used in experiment. The analysis of a single dipole source at different positions on the surface or inside a microsphere, serves to assess the relative efficiency of nearby radiating TE and TM modes, characterizing the profile of the spectrum. By varying the number, positions and alignments of the dipole sources, different excitation scenarios can be compared to analytic models, and to experimental results. The energy flux is collected via a nearby disk-shaped region. The resultant spectral profile shows a dependence on the configuration of the dipole sources. The power outcoupling can then be optimized for specific modes and wavelength regions. The development of such a computational tool can aid the preparation of optical sensors prior to fabrication, by preselecting desired the optical properties of the resonator.

physics.optics↗

arXiv2014

On the Structure of the Lambda 1405

For almost 50 years the structure of the Lambda 1405 resonance has been a mystery. Recently, a new lattice QCD simulation showing that its strange magnetic form factor vanishes, together with a comprehensive Hamiltonian analysis of the lattice QCD energy levels, has unambiguously established that the structure is dominated by a bound anti-kaon--nucleon component [1]. Here we present supplementary information for Ref. [1] including a presentation of the relevant Hamiltonian effective field theory and an illustration of the volume dependence of the results and their connection to the infinite volume limit of Nature.

hep-lat↗

arXiv2013

Pion-mass dispersion relation in the baryon sector

By looking at the complex plane of the pion-mass squared we establish a dispersion relation which the static quantities, such as baryon masses, magnetic moments, polarizabilities, should obey. This dispersion relation yields insight into the differences between the heavy-baryon and relativistic calculations in the baryon sector of chiral perturbation theory.

nucl-th↗

arXiv2011

Ph.D. Thesis: Chiral Effective Field Theory Beyond the Power-Counting Regime

Novel techniques are presented, which identify the power-counting regime (PCR) of chiral effective field theory, and allow the use of lattice quantum chromodynamics results that extend outside the PCR. By analyzing the renormalization of low-energy coefficients of the chiral expansion of the nucleon mass, the existence of an optimal regularization scale is realized. The techniques developed for the nucleon mass renormalization are then applied to a test case: performing a chiral extrapolation without prior phenomenological bias. The robustness of the procedure for obtaining an optimal regularization scale and performing a reliable chiral extrapolation is confirmed. The procedure developed is then applied to the magnetic moment and the electric charge radius of the nucleon. The consistency of the results for the value of the optimal regularization scale provides strong evidence for the existence of an intrinsic energy scale in the nucleon-pion interaction.

hep-lat↗

arXiv2011

Chiral effective field theory beyond the power-counting regime

Novel techniques are presented, which identify the chiral power-counting regime (PCR), and realize the existence of an intrinsic energy scale embedded in lattice QCD results that extend outside the PCR. The nucleon mass is considered as a benchmark for illustrating this new approach. Using finite-range regularization, an optimal regularization scale can be extracted from lattice simulation results by analyzing the renormalization of the low energy coefficients. The optimal scale allows a description of lattice simulation results that extend beyond the PCR by quantifying and thus handling any scheme-dependence. Preliminary results for the nucleon magnetic moment are also examined, and a consistent optimal regularization scale is obtained. This indicates the existence of an intrinsic scale corresponding to the finite size of the source of the pion cloud.

hep-lat↗

arXiv2009

Towards selecting a finite-range regularization scale

Extensive studies have demonstrated that finite-range regularization (FRR) offers significantly improved chiral extrapolations for lattice QCD. These studies have typically relied on selecting the finite-regularization scale based upon phenomenological input. Here we report on a preliminary investigation of a procedure to determine a preferred range of FRR scale based on nonperturbative lattice results -- without any phenomenological prejudice.

hep-lat↗