On the Limitations of the Theory of the Positron

In a recent paper Dirac has suggested a further development of his theory of the positron. Dirac here considers the operators corresponding to charge and current density for a system of electrons in which nearly all the negative energy states are full, and shows that in the presence of an arbitrary external electromagnetic field these operators may be divided into two terms: one of these is infinite, and depends on the field but not on the state of the electrons; the other is finite and determinate, and depends on the field and on the electron state. Dirac makes the suggestion that these second terms be regarded as giving the charge and current density of the electron-positron distribution (epd): i.e., that the formalism of his theory of the electron be modified by the subtraction from the operators for charge and current density of the infinite and field-dependent terms. This modification leaves unaltered the Lorentz and gauge invariance of the theory and the validity of the conservation law for charge and current. Because, however, the way in which the operators are to be modified depends upon the value of the electromagnetic field, the method is not readily extended to take account of the field produced by the epd; on the other hand, it gives for the charge and current induced in the epd by an external field finite and definite results, and thus constitutes in this respect a true theoretical advance

Singularity-Free Electrodynamics for Point Charges and Dipoles: Classical Model for Electron Self-Energy and Spin

It is shown how point charges and point dipoles with finite self-energies can be accomodated into classical electrodynamics. The key idea is the introduction of constitutive relations for the electromagnetic vacuum, which actually mirrors the physical reality of vacuum polarization. Our results reduce to conventional electrodynamics for scales large compared to the classical electron radius $r_0\approx 2.8\times10^{-13}$ cm. A classical simulation for a structureless electron is proposed, with the appropriate values of mass, spin and magnetic moment.Comment: 3 page

Vacuum Polarization and the Electric Charge of the Positron

We show that higher-order vacuum polarization would contribute a measureable net charge to atoms, if the charges of electrons and positrons do not balance precisely. We obtain the limit $|Q_e+Q_{\bar e}| < 10^{-18} e$ for the sum of the charges of electron and positron. This also constitutes a new bound on certain violations of PCT invariance.Comment: 9 pages, 1 figure attached as PostScript file, DUKE-TH-92-38. Revised versio

Measured quantum probability distribution functions for Brownian motion

The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath.Comment: Phys. Rev. A, in pres

Aharonov-Bohm interference in the presence of metallic mesoscopic cylinders

This work studies the interference of electrons in the presence of a line of magnetic flux surrounded by a normal-conducting mesoscopic cylinder at low temperature. It is found that, while there is a supplementary phase contribution from each electron of the mesoscopic cylinder, the sum of these individual supplementary phases is equal to zero, so that the presence of a normal-conducting mesoscopic ring at low temperature does not change the Aharonov-Bohm interference pattern of the incident electron. It is shown that it is not possible to ascertain by experimental observation that the shielding electrons have responded to the field of an incident electron, and at the same time to preserve the interference pattern of the incident electron. It is also shown that the measuring of the transient magnetic field in the region between the two paths of an electron interference experiment with an accuracy at least equal to the magnetic field of the incident electron generates a phase uncertainty which destroys the interference pattern.Comment: 15 pages, 5 Postscript figure

Bell inequality and CP violation in the neutral kaon system

For the entangled neutral kaon system we formulate a Bell inequality sensitive to CP violation in mixing. Via this Bell inequality we obtain a bound on the leptonic CP asymmetry which is violated by experimental data. Furthermore, we connect the Bell inequality with a decoherence approach and find a lower bound on the decoherence parameter which practically corresponds to Furry's hypothesis.Comment: 10 pages, latex, no figure

Parton Branching in Color Mutation Model

The soft production problem in hadronic collisions as described in the eikonal color mutation branching model is improved in the way that the initial parton distribution is treated. Furry branching of the partons is considered as a means of describing the nonperturbative process of parton reproduction in soft interaction. The values of all the moments, and $C_q$, for q=2,...,5, as well as their energy dependences can be correctly determined by the use of only two parameters.Comment: 8 pages (LaTeX) + 2 figures (ps files), submitted to Phys. Rev.

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

The decay constants of pseudoscalar mesons in a relativistic quark model

The decay constants of pseudoscalar mesons are calculated in a relativistic quark model which assumes that mesons are made of a valence quark antiquark pair and of an effective vacuum like component. The results are given in terms of quark masses and of some free parameters entering the expression of the internal wave functions of the mesons. By using the pion and kaon decay constants $F_{\pi^+}=130.7~MeV,~F_{K^+}=159.8~MeV$ to fix the parameters of the model one gets $60~MeV\leq F_{D^+}\leq 185~MeV,~95~MeV\leq F_{D_s}\leq230~MeV,~80~MeV\leq F_{B^+}\leq205~MeV$ for the light quark masses $m_u=5.1~MeV,~m_d=9.3~MeV,~m_s=175~MeV$ and the heavy quark masses in the range: $1.~GeV\leq m_c\leq1.6~GeV,~4.1~GeV\leq m_b\leq4.5~GeV$. In the case of light neutral mesons one obtains with the same set of parameters $F_{\pi^0}\approx 138~MeV,~F_\eta\approx~130~MeV,F_{\eta'} \approx~78~MeV$. The values are in agreement with the experimental data and other theoretical results.Comment: 11 pages, LaTe