arXiv subjects

Dallas C. Kennedy

Publications and source records attributed to Dallas C. Kennedy.

At least 19 recordsLinked to original sources

arXiv2012

How Scaling Symmetry Solves a Second-Order Differential Equation

While not generally a conservation law, any symmetry of the equations of motion implies a useful reduction of any second-order equationto a first-order equation between invariants, whose solutions (first integrals) can then be integrated by quadrature (Lie's Theorem on the solvability of differential equations). We illustrate this theorem by applying scale invariance to the equations for the hydrostatic equilibrium of stars in local thermodynamic equilibrium: Scaling symmetry reduces the Lane-Emden equation to a first-order equation between scale invariants un; vn, whose phase diagram encapsulates all the properties of index-n polytropes. From this reduced equation, we obtain the regular (Emden) solutions and demonstrate graphically how they transform under scale transformations.

math-ph↗

arXiv2012

Scaling Symmetry and Integrable Spherical Hydrostatics

Any symmetry reduces a second-order differential equation to a first integral: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion (exemplified by scale-invariant hydrostatics) yield first-order {\em non-conservation laws} between invariants. We obtain these non-conservation laws by extending Noether's Theorem to non-variational symmetries and present an innovative variational formulation of spherical adiabatic hydrostatics. For the scale-invariant case, this novel synthesis of group theory, hydrostatics, and astrophysics allows us to recover all the known properties of polytropes and define a {\em core radius}, inside which polytropes of index $n$ share a common core mass density structure, and outside of which their envelopes differ. The Emden solutions (regular solutions of the Lane-Emden equation) are obtained, along with useful approximations. An appendix discusses the $n=3$ polytrope in order to emphasize how the same mechanical structure allows different thermal structures in relativistic degenerate white dwarfs and zero age main sequence stars.

math-ph↗

arXiv2010

Scale invariant stellar structure

In scale invariant hydrostatic barotropes, the radial evolutionary equation linearly relates the local gravitational and internal energies. From this first-order equation, directly follow all the properties of polytropes and the important mass-radius relation. Quadrature then leads to the regular Lane-Emden functions and their Picard and Pade approximations, which are useful wherever stars are approximately or exactly polytropic. We illustrate this particularly for the n=3 regular polytrope and obtain analytic approximations to the solution of the Lane-Emden equation, valid over the bulk of relativistic degenerate stars (massive white dwarfs) and chemically homogeneous stars in radiative equilibrium (ZAMS stars).

physics.class-ph↗

arXiv2010

Invariant relationships deriving from classical scaling transformations

Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to evolutionary laws that prove useful, even if the transformations are not generalized symmetries of the equations of motion. In the case of scaling, symmetry leads to a scaling evolutionary law, a first-order equation in terms of scale invariants, linearly relating kinematic and dynamic degrees of freedom. This scaling evolutionary law appears in dynamical and in static systems. Applied to dynamical central-force systems, the scaling evolutionary equation leads to generalized virial laws, which linearly connect the kinetic and potential energies. Applied to barotropic hydrostatic spheres, the scaling evolutionary equation linearly connects the gravitational and internal energy densities. This implies well-known properties of polytropes, describing degenerate stars and chemically homogeneous non-degenerate stellar cores.

physics.class-ph↗

arXiv2010

Classical Scaling Symmetry Implies Useful Nonconservation Laws

Scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action and do not lead to conservation laws. Nevertheless, by an extension of Noether's theorem, scaling symmetries lead to useful {\em nonconservation} laws, which still reduce the Euler-Lagrange equations to first order in terms of scale invariants. We illustrate scaling symmetry dynamically and statically. Applied dynamically to systems of bodies interacting via central forces, the nonconservation law is Lagrange's identity, leading to generalized virial laws. Applied to self-gravitating spheres in hydrostatic equilibrium, the nonconservation law leads to well-known properties of polytropes describing degenerate stars and chemically homogeneous nondegenerate stellar cores.

physics.class-ph↗

arXiv2003

How Hot Is Radiation?

A self-consistent approach to nonequilibrium radiation temperature is introduced using the distribution of the energy over states. We begin rigorously with ensembles of Hilbert spaces and end with practical examples based mainly on the far from equilibrium radiation of lasers. We show that very high, but not infinite, laser radiation temperatures depend on intensity and frequency. Heuristic "temperatures" derived from a misapplication of equilibrium arguments are shown to be incorrect. More general conditions for the validity of nonequilibrium temperatures are also established.

cond-mat.stat-mech↗

arXiv2000

Minimum Entropy Production of Neutrino Radiation in the Steady State

A thermodynamical minimum principle valid for photon radiation is shown to hold for arbitrary geometries. It is successfully extended to neutrinos, in the zero mass and chemical potential case, following a parallel development of photon and neutrino statistics. This minimum principle stems more from that of Planck than that of classical Onsager- Prigogine irreversible thermodynamics. Its extension from bosons to fermions suggests that it may have a still wider validity.

astro-ph↗

arXiv2000

Electroweak Flavor-Conserving Gauge Processes: Virtual Effects

Summary of electroweak Standard Model, including aspects of gauge summetry, symmetry breaking, and quantum radiative corrections. Implications of precise electroweak measurements for Standard Model and hypothetical non-Standard states and interactions. Status of exact and approximate symmetries of the Standard Model. The minimal electroweak Standard Model satisfies the present data well, if the effect of the known top quark mass is included. Contribution to the APS/DPF Drell Panel Study of American High Energy Physics.

hep-ph↗

arXiv2000

Gauge Boson and Fermion Masses Without a Higgs Field

A simple, anomaly-free chiral gauge theory can be perturbatively quantised and renormalised in such a way as to generate fermion and gauge boson masses. This development exploits certain freedoms inherent in choosing the unperturbed Lagrangian and in the renormalisation procedure. Apart from its intrinsic interest, such a mechanism might be employed in electroweak gauge theory to generate fermion and gauge boson masses without a Higgs sector.

hep-th↗

arXiv2000

Solar Core Homology, Solar Neutrinos and Helioseismology

Precise numerical standard solar models (SSMs) now agree with one another and with helioseismological observations in the convective and outer radiative zones. Nevertheless these models obscure how luminosity, neutrino production and g-mode core helioseismology depend on such inputs as opacity and nuclear cross sections. Although the Sun is not homologous, its inner core by itself is chemically evolved and almost homologous, because of its compactness, radiative energy transport, and ppI-dominated luminosity production. We apply luminosity-fixed homology transformations to the core to estimate theoretical uncertainties in the SSM and to obtain a broad class of non-SSMs, parametrized by central temperature and density and purely radiative energy transport in the core.

astro-ph↗

arXiv2000

Variational Principles for Stellar Structure

The four equations of stellar structure are reformulated as two alternate pairs of variational principles. Different thermodynamic representations lead to the same hydromechanical equations, but the thermal equations require, not the entropy, but the temperature as the thermal field variable. Our treatment emphasizes the hydrostatic energy and the entropy production rate of luminosity produced and transported. The conceptual and calculational advantages of integral over differential formulations of stellar structure are discussed along with the difficulties in describing stellar chemical evolution by variational principles.

astro-ph↗

arXiv2000

Analytic Models for the Mechanical Structure of the Solar Core

All stars exhibit universal central behavior in terms of new homology variables (u,w). In terms of these variables, we obtain simple analytic fits to numerical standard solar models for the core and radiative zones of the ZAMS and present Suns, with a few global parameters. With these analytic fits, different theoretical models of the solar core, neutrino fluxes, and helioseismic observations can be parametrized and compared.

astro-ph↗

arXiv2000

A New Limit on the Antiproton Lifetime

Measurements of the cosmic ray pbar/p ratio are compared to predictions from an inhomogeneous disk-diffusion model of pbar production and propagation within the Galaxy, combined with a calculation of the modulation of the interstellar cosmic ray spectra as the particles propagate through the heliosphere to the Earth. The predictions agree with the observed pbar/p spectrum. Adding a finite pbar lifetime to the model, we obtain the limit tau_pbar > 0.8 Myr (90 % C.L.).

astro-ph↗

arXiv2000

Simple Seismic Tests of the Solar Core

A model-independent reconstruction of mechanical profiles (density, pressure) of the solar interior is outlined using the adiabatic sound speed and bouyancy frequency profiles. These can be inferred from helioseismology if both p- and g-mode frequencies are measured. A simulated reconstruction is presented using a solar model bouyancy frequency and available sound speed data.

astro-ph↗

arXiv2000

CPT- and B-Violation: The p-pbar Sector

The CPT symmetry of relativistic quantum field theory requires the total lifetimes of particles and antiparticles be equal. Detection of pbar lifetime shorter than tau_p > O(10^32) yr would signal breakdown of CPT invariance, in combination with B-violation. The best current limit on tau_pbar, inferred from cosmic ray measurements, is about one Myr, placing lower limits on CPT-violating scales that depend on the exact mechanism. Paths to CPT breakdown within and outside ordinary quantum mechanics are sketched. Many of the limiting CPT-violating scales in pbar decay lie within the weak-to-Planck range.

hep-ph↗

arXiv2000

Electroweak Theory Without Higgs Bosons

A perturbative SU(2)_L X U(1)_Y electroweak theory containing W, Z, photon, ghost, lepton and quark fields, but no Higgs or other fields, gives masses to W, Z and the non-neutrino fermions by means of an unconventional choice for the unperturbed Lagrangian and a novel method of renormalisation. The renormalisation extends to all orders. The masses emerge on renormalisation to one loop. To one loop the neutrinos are massless, the A -> Z transition drops out of the theory, the d quark is unstable and S-matrix elements are independent of the gauge parameter xi.

hep-ph↗

arXiv2000

Relativistic electrons on a rotating spherical magnetic dipole: surface orbitals

The semiclassical orbitals of a relativistic electron on a rotating sphere threaded by an intense magnetic dipole field are examined. Several physically distinct regimes emerge, depending on the relative sizes of the mass, total energy, canonical azimuthal angular momentum, and magnetic field strength. Magnetic flux enclosed by orbits is quantized very close to the poles, suggesting a quantum Hall-like state. Application of this system to neutron star surfaces is outlined. The semiclassical orbitals of a relativistic electron on a rotating sphere threaded by an intense magnetic dipole field are examined. Several physically distinct regimes emerge, depending on the relative sizes of the mass, total energy, canonical azimuthal angular momentum, and magnetic field strength. Magnetic flux enclosed by orbits is quantized very close to the poles, suggesting a quantum Hall-like state. Application of this system to neutron star surfaces is outlined.

astro-ph↗

arXiv2000

Relativistic electrons in a rotating spherical magnetic dipole: localized three-dimensional states

Paralleling a previous paper, we examine single- and many-body states of relativistic electrons in an intense, rotating magnetic dipole field. Single-body orbitals are derived semiclassically and then applied to the many-body case via the Thomas-Fermi approximation. The many-body case is reminiscent of the quantum Hall state. Electrons in a realistic neutron star crust are considered with both fixed density profiles and constant Fermi energy. In the first case, applicable to young neutron star crusts, the varying magnetic field and relativistic Coriolis correction lead to a varying Fermi energy and macroscopic currents. In the second, relevant to older crusts, the electron density is redistributed by the magnetic field.

astro-ph↗