Related papers: The Dirac Equation Revisited
By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear…
It is proposed that the Dirac equation, as normally interpreted, incorporates intrinsic redundancies whose removal necessarily leads to an enormous gain in calculating power and physical interpretation. Streamlined versions of the Dirac…
An unconventional outlook on relationship between the quantum mechanics and special relativity is proposed. We show that the two fundamental postulates of quantum mechanics of Planck and de Broglie combined with the idea of comparison scale…
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…
This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…
We reexamine the model of relativistic particle with higher-derivative term linear on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here.…
Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time…
We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal…
This article is a pedagogical introduction to relativistic quantum mechanics of the free Majorana particle. This relatively simple theory differs from the well-known quantum mechanics of the Dirac particle in several important aspects. We…
This paper describes a tentative relativistic quantum mechanics approach inspired by Dirac's point-form, which is based on the physics description on a hyperboloid surface. It is mainly characterized by a non-standard relation of the…
A realization of a deformed Lorentz algebra is considered and its irreducible representations are found; in the limit $q\to 1$, these are precisely the irreducible representations of the classical Lorentz group.
Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of Special Relativity (SR) has been shown to provide a unified origin for the existence of Dirac's Hamiltonian and a self adjoint time operator that…
A causal, non-Hermitian, renormalizable, local, unitary and Lorentz convariant formulation of Quantum Theory (QT) (= Quantum Mechanics (QM) and Quantum Field Theory (QFT)) is developed which is free of formalistic problems we face in the…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
Quantizing the gravitational field described by General relativity being a notorious difficult, unsolved and maybe meaningless problem I use in this essay a different strategy: I consider a linear theory in the framework of Special…
Though the irreducible representations of the Poincare' group form the groundwork for the formulation of relativistic quantum theories of a particle, robust classes of such representations are missed in current formulations of these…
This paper has rather a pedagogical meaning. Surprising symmetries in the $(j,0)\oplus (0,j)$ Lorentz group representation space are analyzed. The aim is to draw reader's attention to the possibility of describing the particle world on the…