Absence of a consistent classical equation of motion for a mass-renormalized point charge

The restrictions of analyticity, relativistic (Born) rigidity, and negligible O(a) terms involved in the evaluation of the self electromagnetic force on an extended charged sphere of radius "a" are explicitly revealed and taken into account in order to obtain a classical equation of motion of the extended charge that is both causal and conserves momentum-energy. Because the power-series expansion used in the evaluation of the self force becomes invalid during transition time intervals immediately following the application and termination of an otherwise analytic externally applied force, transition forces must be included during these transition time intervals to remove the noncausal pre-acceleration and pre-deceleration from the solutions to the equation of motion without the transition forces. For the extended charged sphere, the transition forces can be chosen to maintain conservation of momentum-energy in the causal solutions to the equation of motion within the restrictions of relativistic rigidity and negligible O(a) terms under which the equation of motion is derived. However, it is shown that renormalization of the electrostatic mass to a finite value as the radius of the charge approaches zero introduces a violation of momentum-energy conservation into the causal solutions to the equation of motion of the point charge if the magnitude of the external force becomes too large. That is, the causal classical equation of motion of a point charge with renormalized mass experiences a high acceleration catastrophe.Comment: 13 pages, No figure

Self-forces on extended bodies in electrodynamics

In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion. We place essentially no restrictions (other than boundedness) on the shape of the charge, and allow for inhomogeneity, internal currents, elasticity, and spin. Even if the angular momentum remains small, many such systems are found to be affected by large self-interaction effects beyond the standard Lorentz-Dirac force. These are particularly significant if the particle's charge density fails to be much greater than its 3-current density (or vice versa) in the center-of-mass frame. Additional terms also arise in the equations of motion if the dipole moment is too large, and when the `center-of-electromagnetic mass' is far from the `center-of-bare mass' (roughly speaking). These conditions are often quite restrictive. General equations of motion were also derived under the assumption that the particle can only interact with the radiative component of its self-field. These are much simpler than the equations derived using the full retarded self-field; as are the conditions required to recover the Lorentz-Dirac equation.Comment: 30 pages; significantly improved presentation; accepted for publication in Phys. Rev.

The global electroweak fit at NNLO and prospects for the LHC and ILC

For a long time, global fits of the electroweak sector of the Standard Model (SM) have been used to exploit measurements of electroweak precision observables at lepton colliders (LEP, SLC), together with measurements at hadron colliders (Tevatron, LHC), and accurate theoretical predictions at multi-loop level, to constrain free parameters of the SM, such as the Higgs and top masses. Today, all fundamental SM parameters entering these fits are experimentally determined, including information on the Higgs couplings, and the global fits are used as powerful tools to assess the validity of the theory and to constrain scenarios for new physics. Future measurements at the Large Hadron Collider (LHC) and the International Linear Collider (ILC) promise to improve the experimental precision of key observables used in the fits. This paper presents updated electroweak fit results using newest NNLO theoretical predictions, and prospects for the LHC and ILC. The impact of experimental and theoretical uncertainties is analysed in detail. We compare constraints from the electroweak fit on the Higgs couplings with direct LHC measurements, and examine present and future prospects of these constraints using a model with modified couplings of the Higgs boson to fermions and bosons.Comment: 26 pages, 9 figure

Mild Parkinsonian Signs: A Systematic Review of Clinical, Imaging, and Pathological Associations

Mild parkinsonian signs (MPS) have been widely studied during the past 3 decades and proposed as a risk marker for neurodegenerative disease. This systematic review explores the epidemiology, clinical and prognostic associations, radiological features, and pathological findings associated with MPS in older adults free from neurodegenerative disease. We find that MPS as currently defined are strongly associated with increasing age and increased risk of development of Parkinson's disease (PD), all-cause dementia, disability, and death. Positive associations with later PD are found mainly in younger populations and those with other features of prodromal PD. There are currently no consistent radiological findings for MPS, and pathological studies have shown that MPS, at least in the oldest old, are often underpinned by mixed neuropathologies, including those associated with Alzheimer's disease, cerebrovascular disease, nigral neuronal loss, and Lewy bodies. Different subcategories of MPS appear to convey varying risk and specificity for PD and other outcomes. MPS overall are not specific for parkinsonian disorders and, although associated with increased risk of PD, can reflect multiple pathologies, particularly in older individuals. “Mild motor signs” appears a more appropriate term to avoid prognostic and pathological implications, and larger future studies to prospectively examine outcomes and associations of specific MPS subcategories are required

High energy neutrino yields from astrophysical sources II: Magnetized sources

We calculate the yield of high energy neutrinos produced in astrophysical sources for arbitrary interaction depths $\tau_0$ and magnetic field strengths $B$. We take into account energy loss processes like synchrotron radiation and diffusion of charged particles in turbulent magnetic fields as well as the scattering of secondaries on background photons and the direct production of charm neutrinos. Meson-photon interactions are simulated with an extended version of the SOPHIA model. Diffusion leads to an increased path-length before protons leave the source of size R_s and therefore magnetized sources lose their transparency below the energy $E\sim 10^{18}{\rm eV} (R_s/{\rm pc}) (B/{\rm mG}) \tau_0^{1/\alpha}$, with $\alpha=1/3$ and 1 for Kolmogorov and Bohm diffusion, respectively. Moreover, the neutrino flux is suppressed above the energy where synchrotron energy losses become important for charged particles. As a consequence, the energy spectrum and the flavor composition of neutrinos are strongly modified both at low and high energies even for sources with \tau_0\lsim 1.Comment: 15 pages, 16 figure

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include

New Exclusion Limits for the Search of Scalar and Pseudoscalar Axion-Like Particles from "Light Shining Through a Wall"

Physics beyond the Standard Model predicts the possible existence of new particles that can be searched at the low energy frontier in the sub-eV range. The OSQAR photon regeneration experiment looks for "Light Shining through a Wall" from the quantum oscillation of optical photons into "Weakly Interacting Sub-eV Particles", such as axion or Axion-Like Particles (ALPs), in a 9 T transverse magnetic field over the unprecedented length of $2 \times 14.3$ m. In 2014, this experiment has been run with an outstanding sensitivity, using an 18.5 W continuous wave laser emitting in the green at the single wavelength of 532 nm. No regenerated photons have been detected after the wall, pushing the limits for the existence of axions and ALPs down to an unprecedented level for such a type of laboratory experiment. The di-photon couplings of possible pseudo-scalar and scalar ALPs can be constrained in the nearly massless limit to be less than $3.5\cdot 10^{-8}$ GeV$^{-1}$ and $3.2\cdot 10^{-8}$ GeV$^{-1}$, respectively, at 95% Confidence Level.Comment: 6 pages, 6 figure

Self-forces from generalized Killing fields

A non-perturbative formalism is developed that simplifies the understanding of self-forces and self-torques acting on extended scalar charges in curved spacetimes. Laws of motion are locally derived using momenta generated by a set of generalized Killing fields. Self-interactions that may be interpreted as arising from the details of a body's internal structure are shown to have very simple geometric and physical interpretations. Certain modifications to the usual definition for a center-of-mass are identified that significantly simplify the motions of charges with strong self-fields. A derivation is also provided for a generalized form of the Detweiler-Whiting axiom that pointlike charges should react only to the so-called regular component of their self-field. Standard results are shown to be recovered for sufficiently small charge distributions.Comment: 21 page