Related papers: Wigner's Sisters
Dirac spinors are important objects in the current literature, the algebraic structure presented in the text-books is a general method to write it, however, not unique. The purpose of the present work is to show an alternative approach to…
Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and…
Henri Poincar\'e formulated the mathematics of Lorentz transformations, known as the Poincar\'e group. He also formulated the Poincar\'e sphere for polarization optics. It is shown that these two mathematical instruments can be derived from…
The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he…
Strong field physics close to or above the Schwinger limit are typically studied with vacuum as initial condition, or by considering test particle dynamics. However, with a plasma present initially, quantum relativistic mechanisms such as…
This text offers a personal account of the scientific legacy of two giants of mathematical physics at the turn of the Millenium and their heritage in Canada, their land of adoption.
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
The oscillator-like interaction is introduced in the equation for the particle of arbitrary spin, given by Dirac and re-written to a matrix form by Dowker.
Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing himself successively as a radio astronomer, space physicist and cosmologist, and making a lasting impact on each field. We focus in this…
We prove the following theorem: the Dirac equation for an electron (invented by P.A.M.Dirac in 1928) can be written as a tensor equation. An equation is called a tensor equation if all values in it are tensors and all operations in it take…
The idea of wave mechanics leads naturally to assume the well-known relation $E=\hbar \omega $ in the specific form $H=\hbar W$, where $H$ is the classical Hamiltonian of a particle and $W$ is the dispersion relation of the sought-for wave…
In 1927 the great physicist Paul A. M. Dirac failed to provide a consistent quantum description of the phase of a radiation field. Only one year later, he developed the famous Dirac theory of the electron, which led to the anti-particle --…
We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regu-larised vacuum energy. The leading order of this expansion is given by a classical formula due to…
We present various generalizations of the Dirac formalism. The different-parity solutions of the Weinberg's 2(2J+1)-component equations are found. On this basis, generalizations of the Bargmann-Wigner (BW) formalism are proposed. Relations…
A universal quantum wave equation that yields Dirac, Klein-Gordon, Schrodinger and quantum heat equations is derived. These equations are related by complex transformation of space, time and mass. The new symmetry exhibited by these…
The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…
The equations for various spin particles with oscillator-like interactions are discussed in this talk. Contents: 1. Comment on "The Klein-Gordon Oscillator"; 2. The Dirac oscillator in quaternion form; 3. The Dirac-Dowker oscillator; 4. The…
By analyzing the Dirac equation with static electric and magnetic fields it is shown that Dirac's theory is nothing but a generalized one-particle quantum theory compatible with the special theory of relativity. This equation describes a…
One key theme of Basil Hiley's work was the development of David Bohm's approach to Quantum Mechanics; in particular the concept of the quantum potential. Another theme was the importance of Clifford Algebras in fundamental physics. In this…
In Westminster Abbey, in a nave near to Newton's monument, lies a memorial stone to Paul Dirac. The inscription on the stone includes the relativistic wave equation for an electron: the Dirac equation. At the turn of the 21st century, it…