We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a Schrödinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics.
The Born-Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the relativistic Dirac equation, and a form of the Born-Infeld potential that approximates the self-field corrections of the electron. Using these together, we can establish that if the Born-Infeld nonlinear electrodynamics is to be physically relevant, it must contain a fundamental constant that is well below the original value proposed by Born. This work exten…
We present a general analytical approach to investigate relativistic corrections in the dynamical Casimir effect (DCE). Particularly, we discuss the behavior of the additional frequency bands that appear in the spectral distribution of the created particles when the first relativistic corrections are taken into account. We do that in the context of circuit QED, by analyzing the setup used in the first measurement of the DCE, where a system with a time-dependent boundary condition simulates the mechanical motion of a single mirror in 1+1 dimensions. Our method is applicable to a large class of …
The incoherent, inelastic part of the resonance fluorescence spectrum of a laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. Starting from this level of description, we discuss theoretical foundations of high-precision spectroscopy using the resonance fluorescence light of strongly laser-driven atoms. Specifically, we evaluate the leading relativistic and radiative corrections to the Mollow spectrum, up to the relative orders of (Z alpha)^2 and alpha(Z alpha)^2, respectively, and Bloch-Siegert shifts as well as stimulated radiative corrections invol…
We extend the "gauge choice" problem Lamb noticed to include a time-dependent relativistic non-perturbative Coulomb field, which can be produced by a cluster of relativistic charged particles. If adiabatic conditions are carefully maintained, such a field must be included along side the nuclear Coulomb potential when defining the atomic state. We reveal that when taking the external field approximation, the gauge choice for this time-dependent relativistic non-perturbative Coulomb field cannot be overcome by previous method, and leads to considerable gauge-dependence of the transient spontaneo…
The variational method in a reformulated Hamiltonian formalism of Quantum Electrodynamics is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels of these equations include one-photon exchange interactions. The equations have the expected Schroedinger non-relativistic limit. Application to some exotic few lepton systems is discussed briefly.
We study the photon emission rate of a non relativistic charged particle interacting with an external classical noise through its position. Both the particle and the electromagnetic field are quantized. Under only the dipole approximation, the equations of motion can be solved exactly for a free particle, or a particle bounded by an harmonic potential. The physical quantity we will be interested in is the spectrum of the radiation emitted by the particle, due to the interaction with the noise. We will highlight several properties of the spectrum and clarify some issues appeared in the literatu…
Different operators have been suggested in the literature to describe the electron's spin degree of freedom within the relativistic Dirac theory. We compare concrete predictions of the various proposed relativistic spin operators in different physical situations. In particular, we investigate the so-called Pauli, Foldy-Wouthuysen, Czachor, Frenkel, Chakrabarti, Pryce, and Fradkin-Good spin operators. We demonstrate that when a quantum system interacts with electromagnetic potentials the various spin operators predict different expectation values. This is explicitly illustrated for the scatteri…
It has been observed that a quantum theory need not to be Hermitian to have a real spectrum. We study the non-Hermitian relativistic quantum theories for many complex potentials, and we obtain the real relativistic energy eigenvalues and corresponding eigenfunctions of a Dirac charged particle in complex static and spherically symmetric potentials. Complex Dirac-Eckart, complex Dirac-Rosen-Morse II, complex Dirac-Scarf and complex Dirac-Poschl-Teller potential are investigated.
We introduce a modification in the relativistic hamiltonian in such a way that (1) the relativistic Schrödinger equations can always be based on an underlying Lévy process, (2) several families of particles with different rest masses can be selected, and finally (3) the corresponding Feynman diagrams are convergent when we have at least three different masses.
We prove Cwikel-Lieb-Rosenbljum and Lieb-Thirring type bounds on the discrete spectrum of a two-body pair operator and calculate spectral asymptotics for the eigenvalue moments and the local spectral density in the pseudo-relativistic limit.
We investigate the dynamical Casimir effect for a one-dimensional resonant cavity, with one oscillating mirror. Specifically, we study the discrete spectrum of created particles in a region of frequencies above the oscillation frequency $ω_0$ of the mirror. We focus our investigation on an oscillation time equal to $2L_0/c$, where $L_0$ is the initial and final length of the cavity, and $c$ is the speed of light. For this oscillation duration, a field mode, after perturbed by the moving mirror, never meets this mirror in motion again, which allows us to exclude this effect of re-interaction on…
Starting from the relation between the kinetic energy of a free Levy-Schroedinger particle and the logarithmic characteristic of the underlying stochastic process, we show that it is possible to get a precise relation between renormalizable field theories and a specific Levy process. This subsequently leads to a particular cut-off in the perturbative diagrams and can produce a phenomenological mass spectrum that allows an interpretation of quarks and leptons distributed in the three families of the standard model.
In this work, we study the Aharonov-Bohm-Coulomb (ABC) system for a relativistic Dirac particle with position-dependent mass (PDM). To solve our system, we use the left-handed and right-handed projection operators. Next, we explicitly obtain the eigenfunctions and the energy spectrum of the particle. We verify that these eigenfunctions are written in terms of the generalized Laguerre polynomials and the energy spectrum depends on the parameters Z, $Φ_{AB}$ and $κ$. We notice that the parameter $κ$ has the function of increasing the values of the energy levels of the system. In addition, the us…
Energy equipartition is appropriate only for nonrelativistic classical mechanics, but has only limited relevance for a relativistic theory such as classical electrodynamics. In this article, we discuss harmonic-oscillator thermal equilibrium from three different perspectives. First, we contrast the thermal equilibrium of nonrelativistic mechanical oscillators (where point collisions are allowed and frequency is irrelevant) with the equilibrium of relativistic radiation modes (where frequency is crucial). The Rayleigh-Jeans law appears from applying a dipole-radiation approximation to impose th…
We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single-particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic quantum field theory, we construct states describing collisions of several particles, and define the corresponding $S$-matrix. We also obtain some general restrictions on the shape of the energy-momentum spectrum. For the purpose of our analysis we adapt the concepts of almost local observables and energy-momentum transfer (or Arveson spectrum) from relativistic QFT to the la…
Bound State Solutions of the Relativistic Finite-difference Equation for the Ring-shaped Quesne Oscillator Potential
Institute of Physics, Ministry of Science and Education（阿塞拜疆教育与科学部物理研究所）；Center for Theoretical Physics, Khazar University（哈扎尔大学理论物理中心）；Sumgait State University（苏姆盖特国立大学）
A quantum generalization of the Cooper-Fry recipe is proposed. The single-particle spectrum arising from relativistic collisions of particles and nuclei is calculated within the thermal quantum field theory framework. The starting point of consideration is the solution of the initial-value problem of particle emission from a space-like hypersurface. In the following steps, we obtain the single-particle spectrum using the ``smaller'' Green's function associated with the fireball medium. Based on this result, several specific examples of particle emission are considered.
