Related papers: The Relativistic Dirac-Morse Problem via SUSY QM
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
We prove that the classical Dirac equation in the presence of an external (nondynamical) electromagnetic field is a relativistically causal theory. As a corollary, we show that it is impossible to use quantum tunneling to transmit particles…
Commutator anomalies obstruct solving the Wheeler-DeWitt constraint equation in Dirac quantization of quantum gravity-matter theory. When the obstruction is removed, there result quantal modifications to the constraints. The same classical…
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…
Two questions are suggested as having priority when trying to bring together Quantum Mechanics and General Relativity. Both questions have a scope which goes well beyond Physics, and in particular Quantum Mechanics and General Relativity.
A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical…
The Dirac method of quantizing Hamiltonian systems with constraints is applied to the massless Thirring model. We solve the quantum Hamiltonian equation for the energy-momentum tensor and obtain a violation of the classical conservation…
The system of two relativistic particles with einbein fields is quantized as a constrained system.A method of the introduction of the Newton--Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some…
The similarity renormalization group is used to transform a general Dirac Hamiltonian into diagonal form. The diagonal Dirac operator consists of the nonrelativistic term, the spin-orbit term, the dynamical term, and the relativistic…
Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially…
The complex scaling method is applied to study the resonances of a Dirac particle in a Morse potential. The applicability of the method is demonstrated with the results compared with the available data. It is shown that the present…
Morse theoretical ideas are applied to the study of relative equilibria in the planar $n$-vortex problem. For the case of positive circulations, we prove that the Morse index of a critical point of the Hamiltonian restricted to a level…
We use the light-front machinery to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that the usual projection onto the light-front coordinates for…
A new class of semi-analytically solvable MHD alpha^2-dynamos is found based on a global diagonalization of the matrix part of the dynamo differential operator. Close parallels to SUSY QM are used to relate these models to the Dirac…
General relativistic quantum dynamics of twisted (vortex) Dirac particles is constructed. The Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived for a twisted relativistic electron in arbitrary electric…
The black hole physics techniques and results are applied to find the set of the exact solutions of the SU(3)-Yang-Mills equations in Minkowski spacetime in the Lorentz gauge. All the solutions contain only the Coulomb-like or linear in $r$…
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
We consider the Dirac equation with a generalized uncertainty principle in the presence of the Harmonic interaction and an external magnetic field. By doing the study in the momentum space, the problem solved in an exact analytical manner…