Related papers: Avoiding Negative Probabilities in Quantum Mechani…
It is suggested symmetric relative to particles and antiparticles formulation of the Dirac theory, in which the states with negative energy are excluded. The fields of particles and antiparticles are associated with the wave functions, for…
Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the…
The cosmological constant problem is principally concerned with trying to understand how the zero-point energy of quantum fields contributes to gravity. Here we take the approach that by addressing a fundamental unresolved issue in quantum…
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,…
We show that the antisymmetric spinor tensor representation of spin-0 relativistic quantum mechanics provides a conserved current with positive definite timelike component, interpretable as probability density. The construction runs in…
We consider an isotropic and homogeneous universe in loop quantum cosmology. We assume that the matter content of the universe is dominated by dust matter in early time and a phantom matter at late time which constitutes the dark energy…
The domain of wave functions and effective potentials of the Dirac and Klein-Gordon equations for quantum-mechanical particles in static centrally symmetric gravitational fields are analyzed by taking into account the Hilbert causality…
A fundamental belief is that the formulism of relativistic quantum mechanics equations (RQMEs) should remain in low momentum motion. However, it is found that some formulas from RQMEs were lost in Schr\"odinger equation. For example, a free…
It is proved by a functional method that the conventional expression for the Dirac current is the only conserved 4-vector implied by the Dirac equation that is a function of just the quantum state. The demonstration is extended to derive…
Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to properly account for non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions)…
In his analysis of the Classical Theory of Radiating Electrons, Dirac (1938) draws attention to the characteristic instability of solutions to the third order equation of motion. He remarks that changing the sign of the self-force…
We study the thermodynamic quantities such as the Helmholtz free energy, the mean energy and the specific heat for both the Klein-Gordon, and Dirac equations. Our analyze includes two main subsections: ($i$) statistical functions for the…
Dirac's rule in which only special phase space variables should be promoted to operators in canonical quantization is applied to loop quantum gravity. For this theory, Dirac's rule is violated, and as a result loop quantum gravity fails the…
One of the reasons we expect a standard quantum mechanics, which predicts probabilities for alternatives defined on spacelike slices, to be inadequate for quantum gravity is that the notion of ``spacelike'' is ill-defined in a theory where…
Paul A. M. Dirac has been undoubtedly one of the central figures of the last century physics, contributing in several and remarkable ways to the development of Quantum Mechanics (QM); he was also at the centre of an active community of…
Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in…
The diffculties of relativistic particle theories formulated my means of canonical quantization, such as Klein-Gordon and Dirac theories, ultimately led theoretical physicists to turn on quantum field theory to model elementary particle…
In Dirac's hole theory (HT) the vacuum state is generally believed to be the state of minimum energy due to the assumption that the Pauli Exclusion Principle prevents the decay of positive energy electrons into occupied negative energy…
The Klein-Gordon equation is a useful test arena for quantum cosmological models described by the Wheeler-DeWitt equation. We use the decoherent histories approach to quantum theory to obtain the probability that a free relativistic…
In this paper we present a possible origin of dark matter and dark energy from a solution of the Einstein's equation to a primordial universe, which was presented in a previous paper. We also analyze the Dirac's equation in this primordial…