Related papers: An Introduction to Relativistic Quantum Mechanics.…
We introduce spinors, at a level appropriate for an undergraduate or first year graduate course on relativity, astrophysics or particle physics. The treatment assumes very little mathematical knowledge (mainly just vector analysis and some…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…
We search for a possible mathematical formulation of some of the key ideas of the relational interpretation of quantum mechanics and study their consequences. We also briefly overview some proposals of relational quantum mechanics for an…
We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General…
Earlier, we had presented \cite{heuristic} heuristic arguments to show that a {\em natural unification} of the ideas of the quantum theory and those underlying the general principle of relativity is achievable by way of the measure theory…
The quantum hydrodynamic like equations as a function of two real sets of variables, the 4x4 action matrix and the 4 dimensional wave function modulus vector of the Dirac equation, are derived in the present work. The paper shows that in…
We briefly review a perspective along which the Boltzmann-Gibbs statistical mechanics, the strongly chaotic dynamical systems, and the Schroedinger, Klein-Gordon and Dirac partial differential equations are seen as linear physics, and are…
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the…
The experience from Quantum Information has lead us to look at Quantum Theory (QT) and the whole Physics from a different angle. The information-theoretical paradigm---"It from Bit'---prophesied by John Archibald Wheeler is relentlessly…
The gravitational effects in the relativistic quantum mechanics are investigated. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. As a direct application, we analyze…
We consider deformed special relativity (DSR) theories on commutative space-time, perhaps as an first approximation to a noncommutative space-time formulation. The corresponding field theories in general possess derivatives of all orders.…
In this paper, we study the relativistic quantum problem of a particle constrained to a double cone surface. For this purpose, we build the Dirac equation in a curved space using the tetrads formalism. Two cases are analysed. First, we…
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds…
Using condition of relativistic invariance, group theory and Clifford algebra the component Lorentz invariance generalized Dirac equation for a particle with arbitrary mass and spin is suggested, where In the case of half-integral spin…
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the…