Kenneth C. Hines

Response theory of particle-anti-particle plasmas

Abstract The physical motivation for our work on particle-anti-particle systems comes primarily from astrophysical objects such as pulsars and white dwarf stars. We deal first with the longitudinal dielectric response of an electron-positron or pair plasma in zero and non-zero magnetic fields. The response function must be renormalized using the standard techniques of quantum electrodynamics. For zero magnetic field, the dispersion relation and damping for plasma oscillations are given together with the screening potential about a test charge. For the case of non-zero magnetic field, the longitudinal dielectric response function is again calculated after renormalization. The response function takes on a different form depending upon whether the longitudinal oscillations are parallel or perpendicular to the direction of the magnetic field. The real and imaginary parts of the response function are then exhibited for both cases. The next topic is concerned with the plasma thought to exist in the deep interior of neutron stars or in the ephemeral plasmas of heavy ion collisions. Use of the Feshbach-Villars formalism for the Klein-Gordon equation allows for a similar approach to that previously used for the fermion-anti-fermion case. An adaption of the formalism developed here to two-dimensional systems is also given.

Relativistic boson pair plasma

The longitudinal dielectric response function of a relativistic gas consisting of charged bosons together with the corresponding antiparticles is obtained in the random phase approximation. The theory is renormalized and an analysis of the mode structure and damping properties of the plasma is carried out.

Relativistic charged bosons in a magnetic field. I. Wave functions and matrix elements

A system of charged zero‐spin bosons in the presence of a uniform magnetic field is studied using a relativistic spinor formalism. Equations of motion for the relevant operators are developed. The eigenfunctions of two different sets of commuting operators are obtained by the use of ladder operators and also by direct solution of the Klein–Gordon equation in both coordinate and momentum representations. Matrix elements are calculated which will be required in later consideration of the collisionless conductivity and dielectric tensors for the boson–antiboson plasma in a strong magnetic field (see papers II and III in this series).

The physics of Tachyons IV. Tachyon electrodynamics

A new formulation of the theory of tachyons using the same two postulates as in specialrelativity is applied to the electrodynamics of material media. A discussion of Lagrange’s equations and Hamilton’s equations for ‘classical’ charged tachyons shows that such a formalism is a viable approach. An essay is included on why tachyons can be considered to be localised particles for the purpose of calculations. Tachyonic transformations of the electromagneticfields D, P, H and M are shown to be the same as for bradyonic transformations. Examples discussed include the electric dipole moment of a tachyonic current loop, constitutive equations, polarisation in tachyonic dielectric materials and the velocity of light in tachyonic dielectric media. This is followed by discussions of the collision energy loss for charged tachyonsinteracting with a material medium and a mathematical proof that tachyons cannot emit Cherenkov radiation when passing through a bradyonic dielectric medium.

The physics of tachyons III: tachyon electromagnetism

A new formulation of the theory of tachyons using the same two postulates as in special relativity is applied to electromagnetism. Tachyonic transformations of the electromagnetic fields E and B are rigorously derived from Maxwells equations and are shown to be the same as for bradyonic transformations. Tachyonic transformations of current density, charge density, scalar and vector potentials are also derived and discussed. Tachyonic optics and the four-potential of a moving tachyonic charge are also discussed, along with generalised four-vector transformations and electromagnetic four-tensors in extended relativity. Use is made of a switching principle to show how tachyons automatically obey the law of conservation of electric charge in any inertial reference frame, even though the observed tachyon electric charge is not an invariant between observers. The electromagnetic field produced by a charged tachyon takes the form of a Mach cone, inside which the electromagnetic field is real and detectable, while outside the cone the field generated by the tachyon is imaginary and undetectable.

The physics of tachyons II: tachyon dynamics

This paper extends the development of a new formulation of the theory of tachyons to encompass tachyon dynamics. Topics discussed include tachyonic energy and momentum, proper mass, force and acceleration.