Classical and quantum mechanics of free relativistic membranes

Motivated by the theory of relativistic strings, the theory of a two-dimensional relativistic membrane whose action is proportional to the three-dimensional area it traces out in space-time is investigated both in Lagrangian and Hamiltonian formalisms. The quantum theory is developed using Dirac's method for constrained systems and the question of gauge choices is considered in some detail.     

On the accuracy of valence–shell computations for heavy and super–heavy elements

Recent atomic computations on the (super–) heavy elements have raised the expectation that their low–lying excitation and ionization energies can be calculated with an accuracy of a few hundredth of an eV and, hence, that such computations might help in the identification of new lines. For most many–electron atoms, however, the higher–order relativistic and quantum electrodynamical (QED) effects are included so far only in a rather approximate form. Using different model computations for the neutral and weakly ionized ytterbium (Z = 70) and nobelium atoms (Z = 102), it is shown here that QED effects alone may lead to an uncertainty of 20–50 meV for the excitation energies of all super–heavy elements, and that even for highly–correlated wave functions the theoretical predictions are presently not more accurate than about 0.1 eV. Moreover, in order to support forthcoming spectroscopic measurements on the elements beyond Z = 100, detailed computations have been carried out for the two low–lying 1S0 - 1,3P1o excitation energies of nobelium by using systematically enlarged multiconfiguration Dirac–Fock wave functions.     

Magnetoplasmon excitations in quantum dot arrays

Motivated by the far-infrared transmission experiments of Demel et al., we have investigated the magnetoplasmon excitations in an array of quantum dots within the Thomas–Fermi–Dirac–von Weizsäcker (TFDW) approximation. Detailed calculations of the magnetic dispersion and power absorption from a uniform radiation field unambiguously demonstrates that the noncircular symmetry of the individual dots is responsible for the anticrossing behaviour observed in the experiments. The interdot Coulomb interaction is unimportant at the interdot separation of the samples studied.     

Dirac's extended electron model

Dirac's extended electron model is elaborated here both on the classical and quantum level. The classical equations of motion are deduced from Dirac's action principle. It is shown that the model is free of the troublesome runaway solutions in the classical theory. The quantum theory of the radial oscillations is worked out in detail and the spectrum is discussed. The stability of the model is studied and it is found that Dirac's extended electron is unstable against quadrupole deformations.     

Dirac–Kähler Equation

Tensor, matrix, and quaternion formulations of Dirac–Kähler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection matrix-dyads defining all the 16 independent equation solutions are found. A method of computing the traces of 16-dimensional Petiau–Duffin–Kemmer matrix product is considered. We show that the symmetry group of the Dirac–Kähler tensor fields for charged particles is SO(4, 2). The conservation currents corresponding this symmetry are constructed. We analyze transformations of the Lorentz group and quaternion fields. Supersymmetry of the Dirac–Kähler fields with tensor and spinor parameters is investigated. We show the possibility of constructing a gauge model of interacting Dirac–Kähler fields where the gauge group is the noncompact group under consideration.     

Quantum behavior of deterministic systems with information loss: Path integral approach

’t Hooft’s derivation of quantum from classical physics is analyzed by means of the classical path integral of Gozzi et al. It is shown how the key element of this procedure—the loss of information constraint—can be implemented by means of Faddeev–Jackiw’s treatment of constrained systems. It is argued that the emergent quantum systems are identical with systems obtained in Blasone et al. [Phys. Rev. A 71 (2005) 052507] through Dirac–Bergmann’s analysis. We illustrate our approach with two simple examples—free particle and linear harmonic oscillator. Potential Liouville anomalies are shown to be absent.     

Stochastic derivation of the Dirac equation in terms of a fluid of spinning tops endowed with random fluctuations at the velocity of light

If one analyzes the stochastic behaviour of classical “rigid” tops imbedded in Dirac's aether (relativistic thermostat) one obtains (for random jumps at the velocity of light) a probability distribution corresponding to the Feynman-Gell-Mann equation for relativistic spin $\text{1}\text{2}$ particles.     

Relativistic quark potential for the vector mesons

We extend the heavy quark potential recently proposed by Richardson to the light quarks by using Dirac's theory of constraints. Our relativistic version reproduces the ground state spectrum of the light vector mesons while slightly improving Richardson's own results for the ψ and ? systems.     

Semiclassical Correspondence Principle for Charge Motion and Spin Precession in a Homogeneous Magnetic Field

Solutions to the classical equation of charge motion and the Bargmann–Michel–Telegdi spin equation are derived within a semiclassical approximation (for high energy levels) using the associated solutions to the Dirac–Pauli equation.     

A relativistic correction to semiclassical charmonium

It is shown that the relativistic linear potentials, introduced by the author within the particle à la Wheeler-Feynman direct-interaction (AAD) theory, applied to the semiclassically quantized charmonium, yield energy spectrum comparable to that of some known models. Using the expansion of the relativistic linear AAD potentials in powers ofc ^–1, the charmonium spectrum, given as a rule by Bohr-Sommerfeld quantization of circular orbits, is extended up to the second order of relativistic corrections.     

Deformation Dynamics and the Gauss–Bonnet Topological Term in String Theory

We show that there exists a nontrivial contribution on the Witten covariant phase space when the Gauss–Bonnet topological term is added to the Dirac–Nambu–Goto action describing strings, because the geometry of deformations is modified, and on such space we construct a symplectic structure. Future extensions of the present results are outlined.     

QUANTUM MECHANICAL PROBABILITIES AND GENERAL PROBABILISTIC CONSTRAINTS FOR EINSTEIN–PODOLSKY–ROSEN–BOHM EXPERIMENTS

Relativistic causality, namely, the impossibility of signaling at superluminal speeds, restricts the kinds of correlations which can occur between different parts of a composite physical system. Here we establish the basic restrictions which relativistic causality imposes on the joint probabilities involved in an experiment of the Einstein–Podolsky–Rosen–Bohm type. Quantum mechanics, on the other hand, places further restrictions beyond those required by general considerations like causality and consistency. We illustrate this fact by considering the sum of correlations involved in the CHSH inequality. Within the general framework of the CHSH inequality, we also consider the nonlocality theorem derived by Hardy, and discuss the constraints that relativistic causality, on the one hand, and quantum mechanics, on the other hand, impose on it. Finally, we derive a simple inequality which can be used to test quantum mechanics against general probabilistic theories.     

The quantization of a massless relativistic string in a time-like gauge

The massless relativistic string is quantized in a time-like orthonormal gauge. The results are completely equivalent to those obtained in the light-like case. In particular, a strictly canonical quantization procedure succeeds only when the dimension of space-time is 26. The discussion is based on Dirac's formalism for contrained systems and the introduction of classical variables analogous to those defined by Del Giudice, Di Vecchia and Fubini in the dual model.     

Causal non-local character of quantum statistics

Developing Tersoff and Bayers ideas one shows that quantum statistics result from distinguishable particles correlated by causal non-local actions-at-a-distance. The difference between classical and quantum statistics thus results from the uncontrollable non-local character of stochastic interactions connecting particles imbedded in Dirac's random aether.     

Quantum Potential in Relativistic Dynamics

The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential.     

Solitons and supertranslations

We construct the quantum theory for a two-dimensional supersymmetric theory around a supertranslated soliton solution. This is done by using Dirac's method for constrained systems. The fermionic parameter of supertranslation is treated as a collective co-ordinate. The path-integral expression is also obtained.     

Ab initio calculations of electronic structures of SrMoO4 crystals containing F and F color centers

The electronic structures of SrMoO₄ crystals containing F and F⁺ color centers with the lattice structure optimized are studied within the framework of the fully relativistic self-consistent Dirac–Slater theory, using a numerically discrete variational (DV-Xα) method. From the calculation, it is concluded that F and F⁺ color centers have donor energy level in the forbidden band. The electronic transition energies from the donor level to the bottom of the conduction band are 1.855 eV and 2.161 eV, respectively, which correspond to the 670 nm and 575 nm absorption bands. It is predicted that the 670 nm and 575 nm absorption bands originate from the F and F⁺ centers in SrMoO₄ crystals.     

Relation Between Relativistic and Non-Relativistic Quantum Mechanics as Integral Transformation

A formulation of quantum mechanics (QM) in the relativistic configurational space (RCS) is considered. A transformation connecting the non-relativistic QM and relativistic QM (RQM) has been found in an explicit form. This transformation is a direct generalization of the Kontorovich–Lebedev transformation. It is shown also that RCS gives an example of non-commutative geometry over the commutative algebra of functions.