Related papers: Dirac and Majorana Constructs
Understanding the electron clock and the role of complex numbers in quantum mechanics is grounded in the geometry of spacetime, and best expressed with Spacetime Algebra (STA). The efficiency of STA is demonstrated with coordinate-free…
This chapter, from the Routledge Companion to the Philosophy of Physics (Eleanor Knox and Alastair Wilson, eds., 2021), is an overview of the constraints that relativity places on interpretations of quantum theory. It focuses on four main…
The quantum analogs of the N-dimensional Cayley-Klein spaces with different combinations of quantum and Cayley-Klein structures are described for non-minimal multipliers, which include the first and the second powers of contraction…
The present work is a brief review of the progressive search of improper delta-functions which are of interest in Quantum Mechanics and in the problem of motion in General Relativity Theory.
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
The class of the free relativistic covariant equations generated by the fractional powers of the D'Alambertian operator $(\square^{1/n})$ is studied. Meanwhile the equations corresponding to n=1 and 2 (Klein-Gordon and Dirac equations) are…
This colloquium summarizes Dirac's contributions to the discovery of quantum mechanics before he invented his relativistic wave equation.
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
We investigate the feasibility of performing quantum non-demolition (QND) measurements in relativistic quantum systems, using the one-dimensional Dirac oscillator as a specific example. We derive general expressions for its QND observables…
The gravitational effects in the relativistic quantum mechanics are investigated in a relativistically derived version of Heaviside's speculative Gravity (in flat space-time) named here as Maxwellian Gravity. The standard Dirac's approach…
A proposal of how to complete non-relativistic quantum mechanics to a physically meaningful, mathematically precise and logically coherent theory is reviewed. Our proposal leads to a general, non-linear stochastic law for the time-evolution…
Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role,…
Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their…
The Dirac quantization of a 2+1 dimensional bubble is performed. The bubble consists of a string forming a boundary between two regions of space-time with distinct geometries. The ADM constraints are solved and the coupling to the string is…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
After analyzing Dirac's equation, one can suggest that a well-known quantum-mechanical momentum operator is associated with relativistic momentum, rather than with non-relativistic one. Consideration of relativistic energy and momentum…
We present an attempt to formulate the supersymmetric and relativistic quantum mechanics in the sense of realizing supersymmetry on the single particle level, by utilizing the equations of motion which is equivalent to the ordinary 2nd…
In this research, we investigate the quantum and classical phase transitions of the Dirac particles in a homogeneously magnetized curved rotating 2+1 dimensional spacetime. We consider the intricate relationship between geometry and quantum…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…