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This study investigates a modified two-body Dirac equation in (2+1)-dimensional spacetime, inspired by Amelino-Camelia's doubly special relativity (DSR). We begin by deriving a covariant two-body Dirac equation that, in the absence of DSR…
We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3--geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the…
In this paper we compute asymptotics of solutions of the kinetic Fokker-Planck equation with inelastic boundary conditions which indicate that the solutions are nonunique if $r < r_c$. The nonuniqueness is due to the fact that different…
One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac's delta function orthogonality conditions. The states (doublets)…
The general procedure of constructing a consistent covariant Dirac-type bracket for models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
In this brief review, we survey the problem of electrostatic confinement of massless Dirac particles, via a number of exactly solvable one- and two-body models. By considering bound states at zero energy, we present a route to obtain truly…
The semiclassical solution of quantum Dirac constraints in generic constrained system is obtained by directly calculating in the one-loop approximation the gauge field path integral with relativistic gauge fixing procedure. The gauge…
We study the Dirac equation in confining potentials with pure vector coupling, proving the existence of metastable states with longer and longer lifetimes as the non-relativistic limit is approached and eventually merging with continuity…
We investigate the quantum motion of a neutral Dirac particle bouncing on a mirror in curved spacetime. We consider different geometries: Rindler, Kasner-Taub and Schwarzschild, and show how to solve the Dirac equation by using geometrical…
The relativistic two-body system in (1+1)-dimensional quantum electrodynamics is studied. It is proved that the eigenvalue problem for the two-body Hamiltonian without the self-interaction terms reduces to the problem of solving an…
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…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
There is a review of the physical theories needing Dirac-Bergmann theory of constraints at the Hamiltonian level due to the existence of gauge symmetries. It contains: i) the treatment of systems of point particles in special relativity…
The single particle equations describing motion of carriers in external potential in 2D Dirac-like and Kane intrinsic semiconductors are obtained within second quantization method. The terms renormalizing external potential in these…
We investigate the nucleon-nucleon interaction by using the meson exchange model and the two body Dirac equations of constraint dynamics. This approach to the two body problem has been successfully tested for QED and QCD relativistic bound…
The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for…
The two-dimensional Dirac equation has been widely used in graphene physics, the surface of topological insulators, and especially quantum scarring. Although a numerical approach to tackling an arbitrary confining problem was proposed…
It has been recently shown that in order to have Dirac eigenvalues as observables of Euclidean supergravity, certain constraints should be imposed on the covariant phase space as well as on Dirac eigenspinors. We investigate the…
A general procedure of local reduction for the Dirac equation is introduced to study one- and n-body interacting systems. In the one-body case we show that the reduction allows for an approximate solution of the Dirac equation, correlating…