The series Lecture Notes in Chemistry (LNC), reports new developments in chemistry and molecular science quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge for teaching and training purposes. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research. They will serve the following purposes:  • provide an accessible introduction to the field to postgraduate students and nonspecialist researchers from related areas, • provide a source of advanced teaching material for specialized seminars, courses and schools, and • be readily accessible in print and online. The series covers all established fields of chemistry such as analytical chemistry, organic chemistry, inorganic chemistry, physical chemistry including electrochemistry, theoretical and computational chemistry, industrial chemistry, and catalysis. It is also a particularly suitable forum for volumes addressing the interfaces of chemistry with other disciplines, such as biology, medicine, physics, engineering, materials science including polymer and nanoscience, or earth and environmental science.  Both authored and edited volumes will be considered for publication. Edited volumes should however consist of a very limited number of contributions only. Proceedings will not be considered for LNC.  The year 2010 marks the relaunch of LNC.

Lecture notes in Chemistry

This article is divided in five parts, the first one having nothing to do with tachyons. In fact, to prepare the ground, in part I (sect.2) we shall merely show that special relativity - even without tachyons - can be given a form such to describe both particles and antiparticles. Part II is the largest one: initially, after some historical remarks and having revisited the postulates of special relativity, we presnt a review of the elegant ''model theory'' of tachyons in two dimensions; passing then to four dimensions, we review the main results of the classical theory of tachyons that do not depend on the existence of Superluminal reference frames (or that are at least independent of the explicit form of the Superluminal Lorentz ''transformations''). In particular, we discuss how tachyons would look like, i.e. their apparent ''shape''. Last but not least, all the common causality problems are thoroughly solved, on the basis of the previously reviewed tachyon kinematics. Part III deals with tachyons in general relativity; in particular the question of the apparent Superluminal expansions in astrophysics is reviewed. Part IV shows the interesting, possible role of tachyons in elementary-particle physcis and in quantum theory. In part V, the last one, we face the (still open) problem of the Superluminal Lorentz ''transformations'' in four dimensions, by introducing, for instance, an auxiliary six-dimensional space-time, and finally present the electromagnetic theory of tachyons: a theory that can be relevant also from the ''experimental'' point of view.

Classical tachyons and possible applications

In this paper, we use a biquaternion formalism to model vector-sensor signals carrying polarization information. This allows a concise and elegant way of handling signals with eight-dimensional (8-D) vector-valued samples. Using this model, we derive a biquaternionic version of the well-known array processing MUSIC algorithm, and we show its superiority to classically used long-vector approach. New results on biquaternion valued matrix spectral analysis are presented. Of particular interest for the biquaternion MUSIC (BQ-MUSIC) algorithm is the decomposition of the spectral matrix of the data into orthogonal subspaces. We propose an effective algorithm to compute such an orthogonal decomposition of the observation space via the eigenvalue decomposition (EVD) of a Hermitian biquaternionic matrix by means of a newly defined quantity, the quaternion adjoint matrix. The BQ-MUSIC estimator is derived and simulation results illustrate its performances compared with two other approaches in polarized antenna processing (LV-MUSIC and PSA-MUSIC). The proposed algorithm is shown to be superior in several aspects to the existing approaches. Compared with LV-MUSIC, the BQ-MUSIC algorithm is more robust to modelization errors and coherent noise while it can detect less sources. In comparaison with PSA-MUSIC, our approach exhibits more accurate estimation of direction of arrival (DOA) for a small number of sources, while keeping the polarization information accessible.

MUSIC Algorithm for Vector-Sensors Array Using Biquaternions

A new mathematical formulation of classical electrodynamics is presented. In the theory, the nature of Minkowski space, Lorentz transformations and Maxwell's equations is reduced to those of biquaternions and their functions, the theory of functions of a biquaternion variable. Maxwell's equations in vacuum become equivalent to the «regularity condition» for functions of a «real biquaternion» variable in the sense that Cauchy-Riemann equations are the regularity condition for functions of a complex variable. Several applications of the theory are given.

A new formulation of classical electrodynamics

The paper shows how various physical covariance groups: SO(3), the Lorentz group, the general theory of relativity group, the Clifford algebra SU(2) and the conformal group can easily be related to the quaternion group. The quaternion calculus is introduced and several physical applications: crystallography the kinematics of rigid body motion, the Thomas precession the special theory of relatively, classical electromagnetism, the equation of motion of the general theory of relativity, and Dirac's relativistic wave equation are discussed.

https://iopscience.iop.org/article/10.1088/0143-0807/5/1/007/pdf

The quaternion group and modern physics

The 2×2 complex matrix formulation of relativity and the two-component spin-1/2 formalism are merged with the complex quaternion algebra to yield a concise, manifestly covariant formalism of relativistic quantum mechanics. Along with reproducing all the old results of quantum theory, this complex quaternion formulation extends naturally the concept of scalar mass by adding to it orientation- and velocity-dependent parts giving a hyper-mass. The hyper-mass spin-1/2 equation, with the scalar part of the mass set equal to zero, gives a subtle variation on the two-component neutrino theory with very unsubtle consequences, such as an invariant mass parameter which could distinguishv
eandv
μ and elimination of the superposition principle.

Nature's natural numbers - relativistic quantum theory over the ring of complex quaternions

Hamilton's ancient quaternion formalism gave rise to vector analysis. Quaternions resurface once again to suggest relativistic generalizations of quantum theory and a new spin-12 wave equation.

Quaternion quantum theory - new physics or number mysticism?

The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time. This provides a promising framework for further exploration of a unified quantum/gravity theory.

Quaternion wave equations in curved space-time

Maxwell’s eight equations as one quaternion equation

A conserved current is given for the hypermass generalization of the Dirac equation. The generalization of charge to an invariant quaternion is given which provides insight into a new vector space for relativistic quantum theory. This charge generalization also ensures the independence of the eight internal degrees of freedom in the wave equation.

James D. Edmonds

Papers

Nature's natural numbers - relativistic quantum theory over the ring of complex quaternions

Quaternion quantum theory - new physics or number mysticism?

Quaternion wave equations in curved space-time

Maxwell’s eight equations as one quaternion equation

Generalized charge in the eight-component spin 1/2 wave equation