Papers by Stanley A Bruce
Formulation of axion-electrodynamics with Dirac fields
Zeitschrift für Naturforschung A
We propose a straightforward generalization of axion-electrodynamics (AED) for the case in which ... more We propose a straightforward generalization of axion-electrodynamics (AED) for the case in which a lepton Dirac field is present in the U 1 EM ${\left(1\right)}_{\text{EM}}$ gauge-invariant Lagrangian of the closed system. In the associated differential equations of motion we find that variations in the axion field give rise to modifications in the electric current and in the divergence of the axial current. In light of this, we interpret some possible Dark Matter (DM) phenomena. In particular, we discuss on general grounds (i) AED and DM, and (ii) DM axions interacting with leptons in a nonlinear electrodynamics background. We briefly comment on the conceivable application of this model beyond the subject of DM axions realized in condensed-matter physics.
Relativistic electron dynamics in magnetic fields with low-degree of field nonlinearity
Zeitschrift für Naturforschung A
We study the relativistic bound state dynamics of electrons in the presence of electromagnetic fi... more We study the relativistic bound state dynamics of electrons in the presence of electromagnetic fields within the framework of a novel class of nonlinear Dirac wave equations. In 2 + 1 space–time dimensions, we address a specific interacting electron model in a homogeneous magnetic field providing the allowed nonlinear ground-state Landau energy levels. We concentrate on the regime of laboratory high magnetic fields, and thus, comment on the relevance of this approach to study 2D electron systems.
Study of Certain Infinite-Dimensional Lie Algebras
Nonlinear Dirac equations and the electron dynamics in strong magnetic fields
The European Physical Journal Plus, 2021
We propose a novel class of nonlinear Dirac wave equations in $$3+1$$ flat space-time dimensions.... more We propose a novel class of nonlinear Dirac wave equations in $$3+1$$ flat space-time dimensions. Reducing the space dimensions to 2, we study the electron dynamics in an external homogeneous magnetic field for a specific type of one-electron self-interaction providing the possible (nonlinear) ground-state Landau energy levels together with their respective eigenfunctions. We concentrate on the regime of strong magnetic fields and, thus, briefly comment on the relevance of this approach to reveal certain processes thought to occur particularly near the surfaces of magnetars.
Remarks on axion-electrodynamics
Zeitschrift für Naturforschung A, 2021
We propose a simple generalization of axion-electrodynamics (A-ED) for the general case in which ... more We propose a simple generalization of axion-electrodynamics (A-ED) for the general case in which both scalar and pseudoscalar axion-like fields are present in the (scalar) Lagrangian of the system. We make some remarks on the problem of finding solutions to the differential equations of motion characterizing the propagation of coupled axion fields and electromagnetic (EM) waves. Our primary goal (which is not explored here) is to understand and predict novel phenomena that have no counterpart in pseudoscalar A-ED. With this end in view, we discuss on very general grounds possible processes related to scalar (and pseudoscalar) axions, e.g., the Primakoff effect; the Compton scattering; and, notably, the EM two-photon axion decay.
Zeitschrift für Naturforschung A, 2018
In this article, we show that the wave equation for a free Dirac electron can be represented in a... more In this article, we show that the wave equation for a free Dirac electron can be represented in a form that is analogous to Maxwell’s electrodynamics. The electron bispinor wavefunction is explicitly expressed in terms of its real and imaginary components. This leads us to incorporate into it appropriate scalar and pseudo-scalar fields in advance, so that a full symmetry may be accomplished. The Dirac equation then takes on a form similar to that of a set of inhomogeneous Maxwell’s equations involving a particular self-source. We relate plane wave solutions of these equations to waves corresponding to free Dirac electrons, identifying the longitudinal component of the electron motion, together with the corresponding Zitterbewegung (“trembling motion”).
Zeitschrift für Naturforschung A, 2018
It is known that the principle of minimal coupling in quantum mechanics determines a unique inter... more It is known that the principle of minimal coupling in quantum mechanics determines a unique interaction form for a charged particle. By properly redefining the canonical commutation relation between (canonical) conjugate components of position and momentum of the particle, e.g. an electron, we restate the Dirac equation for the hydrogen-like atom problem incorporating a generalized minimal electromagnetic coupling. The corresponding interaction keeps the $1/\left|\mathbf{q}\right|$ dependence in both the scalar potential $V\left({\left|\mathbf{q}\right|}\right)$ and the vector potential $\mathbf{A}\left(\mathbf{q}\right)$ ($\left|{\mathbf{A}\left(\mathbf{q}\right)}\right|\sim 1/\left|\mathbf{q}\right|$). This problem turns out to be exactly solvable; moreover, the eigenstates and eigenvalues can be obtained in an elementary fashion. Some feasible models within this approach are discussed. Then we make a few remarks about the breaking of supersymmetry. Finally, we briefly comment on ...
Zeitschrift für Naturforschung A, 2018
It is known that there is no room for anti-particles within the Schrödinger regime in quantum mec... more It is known that there is no room for anti-particles within the Schrödinger regime in quantum mechanics. In this article, we derive a (non-relativistic) Schrödinger-like wave equation for a spin- 1 / 2 $1/2$ free particle in 3 + 1 space-time dimensions, which includes both positive- and negative-energy eigenstates. We show that, under minimal interactions, this equation is invariant under 𝒫 𝒯 $\mathcal{P}\mathcal{T}$ and 𝒞 discrete symmetries. An immediate consequence of this is that the particle exhibits Zitterbewegung (‘trembling motion’), which arises from the interference of positive- and negative-energy wave function components.
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2008
We explore the feasibility of performing an experiment to measure the interaction of cold neutron... more We explore the feasibility of performing an experiment to measure the interaction of cold neutrons with a given classical electric field. Bound and scattering states could be detected by means of an approximate Aharonov-Casher configuration. The theoretical background is presented and then some primary elements for building a neutron detector of this nature are proposed.
Zeitschrift für Naturforschung A, 2017
We developed certain symmetries in Maxwell’s equations by incorporating (independent) dynamical d... more We developed certain symmetries in Maxwell’s equations by incorporating (independent) dynamical degrees of freedom. Once magnetic monopoles are included, it was assessed whether this system can admit electromagnetic-like scalar and pseudo-scalar fields so that a full symmetry may be accomplished. The result is restated in differential forms. The subsequent generalised classical equations of motion for dyons are displayed. In quantum mechanics, we find that, for a given scalar potential, a critical behaviour does not occur and the Dirac vacuum remains stable: the scalar coupling cannot create spontaneous electron-positron pairs.
Il Nuovo Cimento B, 1995
In this note we show that Weyl's theory of massless neutrinos can be formulated in a form closely... more In this note we show that Weyl's theory of massless neutrinos can be formulated in a form closely parallel to Maxwell's electromagnetism. The neutrino spinor wave function is explicitly represented in terms of its real and imaginary components. The Weyl equation then takes a form similar to a set of inhomogeneous Maxwell equations involving a particular longitudinal source. We relate plane-wave solutions of these equations to those corresponding to actual neutrinos and anti-neutrinos, identifying the spinor components in each case. We briefly comment on the possibility of constructing simple supersymmetric models relating spin-(l/2) and spin-1 fields.
Classical symmetries of a closed bosonic 3-brane
Physics Letters B, 1989
ABSTRACT
Physical Review A, 1999
We consider the problem of the bound states of a spin 1/2 chargless particle in a given Aharonov-... more We consider the problem of the bound states of a spin 1/2 chargless particle in a given Aharonov-Casher configuration. To this end we recast the description of the system in a supersymmetric form. Then the basic physical requirements for unbroken supersymmetry are established. We comment on the possibility of neutron confinement in this system.
Comments on minimal interactions in quantum mechanics
Journal of Physics A: Mathematical and General, 1996
We study minimal interactions in quantum systems characterized by position and momentum operators... more We study minimal interactions in quantum systems characterized by position and momentum operators defined as the direct product of a traceless finite matrix and an ordinary canonical coordinate.
Neutron confinement and the Aharonov–Casher effect
Journal of Physics A: Mathematical and General, 2005
We determine the (bound) ground state of a spin-1/2 chargeless particle with anomalous magnetic m... more We determine the (bound) ground state of a spin-1/2 chargeless particle with anomalous magnetic moment in certain Aharonov–Casher configurations. We recast the description of the system in a supersymmetric form. Then the basic physical requirements for unbroken supersymmetry are established. We comment on the possibility of neutron confinement in these systems.
Algebras for the two-sphere and the three-sphere groups of compact simple Lie groups
Journal of Mathematical Physics, 1990
ABSTRACT
Europhysics Letters (EPL), 1999
We determine the (bound) ground state of a spin 1/2 chargless particle with anomalous magnetic mo... more We determine the (bound) ground state of a spin 1/2 chargless particle with anomalous magnetic moment in certain Aharonov-Casher configurations. We recast the description of the system in a supersymmetric form. Then the basic physical requirements for unbroken supersymmetry are established. We comment on the possibility of neutron trapping in these systems.
Unspread wave packet in quantum mechanics
Canadian Journal of Physics, 1984
The problem of the evolution in time of a quantum mechanical wave packet is restudied. A nondispe... more The problem of the evolution in time of a quantum mechanical wave packet is restudied. A nondispersive wave packet is constructed considering appropriately the transformation rules associated with conveniently defined inertial reference frames.
Neutron bound states in a supersymmetric double Dirac delta electrostatic potential
Annalen der Physik, 2011
ABSTRACT We study neutron bound states in a particular (1 + 1)-supersymmetric configuration. A si... more ABSTRACT We study neutron bound states in a particular (1 + 1)-supersymmetric configuration. A simple physical setup is chosen so that the effective interaction becomes a particular kind of double Dirac delta potential. In this configuration it is shown that the neutron distinguishes between positive and negative electric charge as a consequence of a purely quantum mechanical effect. The theoretical background is presented and a possible application to a real-life physical system is discussed. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Covariant coordinate transformations and scalar-field – matter interactions
Zeitschrift für Naturforschung A
We propose a classical Lorentz invariant model of local scalar-field - matter interactions where ... more We propose a classical Lorentz invariant model of local scalar-field - matter interactions where the zeroth component of the space-time coordinates of a particle is modified by a background Klein–Gordon field. This model is not directly explained in terms of the standard model (SM) because the CPT symmetry is generally broken with a Hermitian Hamiltonian. Our ultimate goal (which is not explored here) is to construct a quantum field theory approach to tackle the matter–antimatter asymmetry problem. To understand the basics of the theory, two examples are discussed only at the quantum mechanical level: (i) a (quantum) harmonic oscillator with the occurrence of negative-energy eigenvalues where the effective energy-masses of the ‘particle and antiparticle’ are not symmetric with respect to the non-physical zero-energy mode of the oscillator; (ii) a Dirac particle in an electromagnetic (EM) linear potential.
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Papers by Stanley A Bruce