Dirac's Hole Research Articles

Observation of Quantum Hall effect in an ultra-thin (Bi0.53Sb0.47)2Te3 film

We report the observation of the Quantum Hall effect from the topological surface states in both the Dirac electron and Dirac hole regions in a 4 quintuple layer (Bi0.53Sb0.47)2Te3 film grown on GaAs (111)B substrates. The Fermi level is sitting within the enlarged bulk band gap due to the quantum confinement of the ultra-thin film and can be tuned through the Dirac point by gate biases. Furthermore, the Hall resistance Rxy shows even denominator plateaus, which could be fractional Quantum Hall states. This may be due to the hybridization between the top and bottom surface states and suggests the possible way to manipulate the interaction of two surfaces for potential spintronic devices.

Large negative numbers in number theory, thermodynamics, information theory, and human thermodynamics

We show how the abstract analytic number theory of Maier, Postnikov, and others can be extended to include negative numbers and apply this to thermodynamics, information theory, and human thermodynamics. In particular, we introduce a certain large number N0 on the “zero level” with a high multiplicity number qi ≫ 1 related to the physical concept of gap in the spectrum. We introduce a general notion of “hole,” similar to the Dirac hole in physics, in the theory. We also consider analogs of thermodynamical notions in human thermodynamics, in particular, in connection with the role of the individual in history.

Theory of photon–electron interaction in single-layer graphene sheet

The purpose of this work is to elaborate the quantum theory of photon–electron interaction in a single-layer graphene sheet. Since the light source must be located outside the extremely thin graphene sheet, the problem must be formulated and solved in the three-dimensional physical space, in which the graphene sheet is a thin plane layer. It is convenient to use the orthogonal coordinate system in which the xOy coordinate plane is located in the middle of the plane graphene sheet and therefore the Oz axis is perpendicular to this plane. For the simplicity we assume that the quantum motions of electron in the directions parallel to the coordinate plane xOy and that along the direction of the Oz axis are independent. Then we have a relatively simple formula for the overall Hamiltonian of the electron gas in the graphene sheet. The explicit expressions of the wave functions of the charge carriers are easily derived. The electron–hole formalism is introduced, and the Hamiltonian of the interaction of some external quantum electromagnetic field with the charge carriers in the graphene sheet is established. From the expression of this interaction Hamiltonian it is straightforward to derive the matrix elements of photons with the Dirac fermion–Dirac hole pairs as well as with the electrons in the quantum well along the direction of the Oz axis.

On the Pauli-Weisskopf anti-Dirac paper

We review in this article the role which the work of Pauli and Weisskopf played in formulating a quantum field theory of spinless particles. To make our computations as transparent as possible, we offer a physicist's derivation of the Klein-Gordon-Fock equation. Since invariant functions play a significant part in our paper, we will discuss them in great detail. We emphasize Pauli's and Weisskopf's view that Dirac's hole theory is totally obsolete in formulating a consistent quantum field theory, be it for scalar or spinor particles. As an important example we present the calculation for producing charged scalar particles in an external electric field.

Dirac sea contribution in the relativistic random phase approximation

In quantum hadrodynamics there are two methods to take account of the contribution of negative-energy states in the relativistic random phase approximation. Dawson and Furnstahl made the ansatz that the Dirac sea was empty, while according to the Dirac hole theory the sea should be fully occupied. The two methods seem contradictory. Their close relationship and compatibility are explored and in particular the question of the ground-state instability resulting from the Dawson–Furnstanhl ansatz is discussed.

Some new results concerning the vacuum in Dirac's hole theory

In Dirac's hole theory (HT), the vacuum state is generally believed to be the state of minimum energy. It will be shown that this is not, in fact, the case and that there must exist states in HT with less energy than the vacuum state. It will be shown that energy can be extracted from the HT vacuum state through application of an electric field.

Some differences between Dirac's hole theory and quantum field theory

Dirac's hole theory (HT) and quantum field theory (QFT) are generally considered equivalent. However, it was recently shown by several investigators that this is not necessarily the case because when the change in the vacuum energy was calculated for a time-independent perturbation, HT and QFT yielded different results. In this paper, we extend this discussion to include a time-dependent perturbation for which the exact solution to the Dirac equation is known. We show that for this case also, HT and QFT yield different results. In addition, we offer some discussion of the problem of anomalies in QFT. PACS Nos.: 03.65–w, 11.10–z

The Concepts of E Infinity: An elementary introduction to the Cantorian-fractal theory of quantum physics

Abstract The paper is an elementary introduction to the concepts of E Infinity of quantum physics. In the first two paragraphs the main concepts of E Infinity theory and some of the principle results have been explained. Subsequently we address the problem of the mass spectrum of the standard model from various viewpoints, in particular, from that of gravitational instanton. Particular attention is paid throughout the paper to giving an intuitive grasp for an extended theory of vacuum fluctuation based on Dirac's hole theory and E Infinity theory. It is further shown how the golden mean and logarithmic scalings can be used to understand quantum gravity and how the new transfinite Dirac's theory can explain certain anomalous positron production which was observed by several experimental groups worldwide.

Some remarks on Dirac's hole theory versus quantum field theory

Dirac's hole theory and quantum field theory are generally considered to be equivalent to each other. However, it has been recently shown that this is not necessarily the case. In this article, we will discuss the reason for this lack of equivalence and suggest a possible solution.PACS Nos.: 03.65.–w, 11.10.–z

Dirac's hole theory versus quantum field theory

Dirac's hole theory and quantum field theory are usually considered equivalent to each other. The equivalence, however, does not necessarily hold, as we discuss in terms of models of a certain type. We further suggest that the equivalence may fail in more general models. This problem is closely related to the validity of the Pauli principle in intermediate states of perturbation theory. PACS Nos.: 03.65-w, 11.10-z, 11.15Bt, 12.39Ba

Composite nucleons and the Dirac sea.

Effects associated with the Dirac sea of nucleons have been proposed as important to several nuclear physics problems. The simplest interpretation of these effects is in terms of virtual NN\ifmmode\bar\else\textasciimacron\fi{} pairs. Here it is argued that the composite nature of the nucleon probably suppresses the contribution of NN\ifmmode\bar\else\textasciimacron\fi{} pairs compared to what is expected in naive Dirac hole theory. This is made plausible by studying tractable systems of interacting composite fermions. These systems include general topological soliton models in 1+1 dimensions, the exactly solvable massive Thirring model and large-${\mathit{N}}_{\mathit{c}}$ QCD. It is convenient to discuss these models in terms of a compositeness parameter c=MR, where M and R are the mass and intrinsic size of the composite fermion. It is found on general theoretical grounds that for these systems in the limit c\ensuremath{\rightarrow}\ensuremath{\infty} the NN\ifmmode\bar\else\textasciimacron\fi{} pairs contributions are smaller than any power law in c. The successful Dirac phenomenology of intermediate energy proton-nucleus scattering can be reconciled with this suppression of virtual NN\ifmmode\bar\else\textasciimacron\fi{}. The ``z graphs'' in the phenomenology, however, should not be interpreted as arising from virtual NN\ifmmode\bar\else\textasciimacron\fi{} pairs. One-nucleon-loop contributions in quantum hadrodynamics do appear to be suppressed.

Normalization of bound-state solutions to the Breit equation.

We derive the spin-(1/2, two-particle Breit equation from the Bethe-Salpeter equation with instantaneous interaction kernel, and solve for the relative time dependence of the resulting Bethe-Salpeter amplitude \ensuremath{\psi}(x). As t\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}, \ensuremath{\psi}(x) increases exponentially in Dirac hole theory, but goes to zero in single-electron theory. Assuming single-electron theory, a normalization condition is derived for \ensuremath{\psi}(r,0), the solution to the Breit equation, from the normalization for the Bethe-Salpeter amplitude.

The Concept of Particle Creation before and after Quantum Mechanics

One of the most important results in the recent development of electron theory, Victor Weisskopf wrote in the mid-thirties, the possibility of transforming electromagnetic field energy into matter. A light quantum, for example, in the presence of other electromag netic fields in empty space, can be absorbed and transformed into matter, with the creation of a pair of electrons with opposite charge.1 By recent, Weisskopf meant the period since P. A. M. Dirac's theory of the electron, which was published in 1928.2 Today, physicists by and large still believe that the concept of the creation of fundamental particles, as well as that of the inverse process of their destruction, is a product of quantum mechanics. In actuality, creation and annihilation concepts antedate quantum mechanics. The concept of the annihilation of pairs of oppositely charged, elementary particles,3 for example, dates from the turn of the twentieth century. It became important in astrophysics about 1924, and continued to be through the early thirties. The annihilat ing pairs were first positive and negative electrons, later protons and electrons, and finally, starting in 1931, electrons and anti-electrons. For the physicists who were building quantum mechanics, the concept was familiar and acceptable, if minor, and they included it in their theories where convenient. In Dirac's hole theory of 1930, for example, pair annihilation was neither novel nor central. Dirac's object was to deal with a difficulty inhering in relativistic electron

THE RADIATIVE CORRECTIONS TO THE SCATTERING OF ELECTRONS AND POSITRONS

With the Mφller's theory of scattering between the electrons and the Dirac's hole theory, Bhabha has obtained the formula for the scattering of the electrons and the positrons. The experimental evidence of this phenomenon was discovered by Ho (何泽慧), and she has studied this phenomenon by means of the β+-radioactivity of the β+ sources such as Mn52, and F18 in the cloud chamber. The comparison of the theory and the experiment was done (see reference [2], [3], [4], [5] and [6].) by Ho, O. Ritter et al, R. R. Roy and L. Groven, G. R. Hoke and A. Ashkin et al.The purpose of the present work is to show the effect of the radiative corrections to the scattering of the electrons and the positrons by the method in the quantum electrodynamics developed by S. Tomonaga, J. Schwinger, R. P. Feynman and F. J. Dyson.In the above-mentioned electron and positron scattering experiments, the contributions to the scattering cross-section are mostly due to the positrons of low energies (about 0.1 to 0.2 Mev). In this energy range, the exchange effect in Bhabha's theory is small. In this work for the radiative corrections to the scattering of the electrons and the positrons, we have neglected this exchange effect. The ratio of the correction of the scattering cross-section due to the radiative corrections to the scattering cross-section of Bhabha's theory at this energy range does not exceed 1%. For experiments of the low energy positrons and of the higher energy positrons (e.g positrons with energies of 0.5 Mev to 1 Mev as in the experiment of Ashkin et al) with small exchanges of energy between the electrons and the positrons during scattering, our calculation is adequate. But for positrons of higher energies and with large exchanges during scattering, our calculation should be improved by considering the exchange effect.

The Electromagnetic Shift of Energy Levels

B very beautiful experiments, Lamb and Retherford1 have shown that the fine structure of the second quantum state of hydrogen does not agree with the prediction of the Dirac theory. The 2s level, which according to Dirac’s theory should coincide with the 2p 1 2 level, is actually higher than the latter by an amount of about 0.033 cm−1 or 1000 megacycles. This discrepancy had long been suspected from spectroscopic measurements.23 However, so far no satisfactory theoretical explanation has been given. Kemble and Present, and Pasternack4 have shown that the shift of the Is level cannot be explained by a nuclear interaction of reasonable magnitude, and Uehling5 has investigated the effect of the “polarization of the vacuum” in the Dirac hole theory, and has found that this effect also is much too small and has, in addition, the wrong sign. Schwinger and Weisskopf, and Oppenheimer have suggested that a possible explanation might be the shift of energy levels by the interaction of the