Session H12: New Directions in Particle Theory

Quantum mechanics using Fradkin's representation

Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum mechanics (field theory in one dimension) and apply it to the solution of Schrodinger's equation for the quantum harmonic oscillator.   

On the Origin of the Klein-Gordon-Dirac expression, and its implication in Particle Mass Ratios

This paper puts fourth the proposition that Klein-Gordon-Dirac wave equation is descended from a more general expression, and the solutions of the more general expression illustrate known particle properties including potentials and mass ratios. The particle solutions of the general expression encompass the particles general properties as well as the electromagnetic interaction. A plausible derivation of the mass ratios for particles is shown to imply certain allowed internal modes, and allows separation of the general equation into periodic and non-periodic equations. The modes and mass ratios are shown for the leptons, the proton, the neutron and the W boson, to a reasonable degree of accuracy.   

Vacuum Structure and Dynamics; Particle Formation

We model the vacuum as filled of neutral vacuuons, each consisting of a p- vaculeon of charge +e at the core and an n- vaculeon of -e on the envelope, mutually bound with a Coulomb energy $\sim 10^6$ J. The model is derived based on overall experimental observations. In particular, as shown in the pair annihilation $e^-+ e^+ \rightarrow \gamma + \gamma $, the two emitted $\gamma$ rays carry the energy ($2 M_e c^2=1022$ keV) converted from the mass $2M_{e^-} $ of $e^-$ and $e^+$ only, whilst the Coulomb potential energy $V = -\frac{e^2}{4 \pi \epsilon_0 r_0}$ between their charges $+ e$ and $-e$ separated at $r_0$, are not released. Energy conservation requires $V$ and its certain carriers must remain in the vacuum after the annihilation. The afore-modeled vacuum will be polarized by the static field of an external charge, induced with a shear elasticity, and thereby able to propagate the disturbances of the charge's accelerating movements as transverse elastic waves---whence the electromagnetic waves. We have given a systematic representation of the statics and dynamics of this vacuum based on classical equations of motion and solutions (JXZJ \& P-IJ, {\it Unification of Classical, Quantum and Relativistic Mechanics and the Four Forces}, Fwd Prof R Lundin, Nova Science, NY, 2005). The solutions in particular yield a basic material particle, like an electron, proton, etc, formed of a massless oscillatory charge and its resulting electromagnetic waves in the vacuum, having the overall observational properties of the basic material particles.   

Multidimensional cut-off technique for Casimir energy of massless scalar fields with applications to Bose-Einstein condensates

Quantum fluctuations of massless scalar fields represented by quantum fluctuations of the quasiparticle vacuum in a zero- temperature weakly-interacting dilute Bose-Einstein condensate (BEC) may well provide the first experimental arena for measuring the Casimir force of a field other than the electromagnetic field. This would constitute a real Casimir force measurement--due to quantum fluctuations--in contrast to thermal fluctuation effects. We develop a multidimensional cut-off technique for calculating the Casimir energy of massless scalar fields in d-dimensional rectangular spaces with arbitrary lengths. We explicitly evaluate the multidimensional remainder and express it in a form that converges exponentially fast. Most importantly, we show that the division between analytical and remainder is not arbitrary but has a natural physical interpretation. The analytical part can be viewed as the sum of individual parallel plate energies and the remainder as an interaction energy. The results are applied to the Casimir force in a zero-temperature weakly-interacting dilute BEC.   

Superluminal Quantum Models of the Electron and the Photon

A spatial model of a free electron (or a positron) is formed by a proposed helically circulating point-like charged superluminal quantum. The model includes the Dirac equation's electron spin $\textstyle{1 \over 2}\hbar $ and magnetic moment $e\hbar /2m$ as well as three Dirac equation measures of the electron's \textit{Zitterbewegung} (jittery motion): a speed of light velocity $c$, a frequency of $2mc^2/h=2.5\times 10^{20}$ hz, and a radius of $\textstyle{1 \over 2}\hbar /mc=1.9\times 10^{-13}$m. The electron's superluminal quantum has a closed double-looped helical trajectory whose circular axis' double-looped length is one Compton wavelength h/mc. The superluminal quantum's maximum speed in the electron model's rest frame is $2.797c$. In the electron model's rest frame, the equations for the superluminal quantum's position are: \[ \begin{array}{l} x(t)=R_0 (1+\sqrt 2 \cos (\omega _0 t))\cos (2\omega _0 t) \\ y(t)=R_0 (1+\sqrt 2 \cos (\omega _0 t))\sin (2\omega _0 t) \\ z(t)=R_0 \sqrt 2 \sin (\omega _0 t) \\ \end{array} \] where $R_0 =\textstyle{1 \over 2}\hbar /mc$ and $\omega _0 =mc^2/\hbar $. A photon is modeled by an uncharged superluminal quantum moving at $1.414c$ along an open 45-degree helical trajectory with radius $R=\lambda /2\pi $. http://www.superluminalquantum.org   

Nonlinear finite self-energy classical electron model

A classical electron model is proposed having finite self-energy $e^2/r_0 $, stability, and Lorentz invariance. The electrostatic field energy density provides a nonlinear spherically symmetric microscopic integrable charge and energy distribution of infinite extent in the rest frame. In motion a coupling equation required for Lorentz invariance is defined between the radius of a spherically symmetric core containing the charge $e$ and rest mass $m_0 $, and its linear velocity v. It separates the charge and rest mass from the exterior electromagnetic field kinetic energy, providing a proxy size, demonstrating point-particle behavior and displaying the Coulomb field. The core radius decreases with increasing v, approaching zero as v$\to $ c. Analogies to the uncertainty principle and Zitterbewegung appear. Results of current theory are unchanged. Although the classical self energy is finite, its Coulomb field will produce some of the divergences encountered in QED. This derivation shows that the theory expands the scope of special relativity beyond point particles to include this class of extended charged particles.   

Chaotic behavior of the renormalization group flow and standard model parameters

Despite years of sustained research efforts, a consistent and comprehensive understanding of standard model parameters is missing. For example, models based on the Higgs doublet or supersymmetry, as well as leptogenesis, grand unification and seesaw mechanisms offer at most an incomplete picture with little or no experimental evidence. Our work suggests that the spectrum of particle masses, gauge couplings and fermion mixing angles may be derived from the chaotic regime of the renormalization group flow. We find that the observed hierarchies of parameters amount to a series of scaling ratios depending on the Feigenbaum constant. Since fermion mass scaling ratios and mixing matrices can be parameterized in terms of the Cabibbo angle, this finding provides a natural connection between the Cabibbo angle and the Feigenbaum constant. Moreover, it is shown that the model can accommodate hypothetical generations of both heavy and ultra-light fermions that are expected to emerge beyond the energy range of the standard model. A representative example in this regard is the fourth family neutrino whose detection is anticipated at future linear colliders.   

Schwinger's Measurement Algebra, Preons and the Lepton Masses

In the 1950s and 1960s, Julian Schwinger developed an elegant general scheme for quantum kinematics and dynamics appropriate to systems with a finite number of dynamical variables, now knowns as ``Schwinger's Measurement Algebra'' (SMA). The SMA has seen little use, largely because it is non relativistic in that it does not allow for particle creation. In this paper, we apply the SMA to the problem of modeling tightly bound subparticles (preons) of the leptons and quarks. We discuss the structure of the ideals of Clifford algebras and, applying this to the elementary fermions, derive a preon substructure for the quarks and leptons. We show that matrices of SMA type elements can be used to model the quarks and leptons under the assumption that the preons are of such high energy that they cannot be created in normal interactions. This gives a definition of the SMA for the composite particle in terms of the SMA of its constituents. We solve the resulting matrix equation for the quarks and leptons. We show that the mass operator for the charged leptons is related to the democratic mass matrix used in the Koide mass formula.   

On The Structure of Leptonic Families and Currents of the Vector Nature

Any of leptonic neutrino similarly to a kind of lepton has a Dirac mass responsible as well as for its Coulomb's behavior. Such a neutrino can possess both electric charge and vector dipole moment. Their form factor appears, for example, at the polarized neutrinos scattering in the field of a spinless nucleus. We derive an equation which relates the masses to a ratio of Dirac and Pauli form factors of each lepton and its neutrino. A new theory of fermions unification is suggested. In this theory, the leptons and their neutrinos are united in families not only of the left - handed $SU(2)_{L}$ - doublets but also of the right - handed $SU(2)_{R}$ - singlets. Thereby it predicts the existence in nature of the right - left dileptons and paradileptons. A formation of any of them is responsible for the legality of conservation of charge, lepton flavors and full lepton number. Therefore, each of earlier measured processes originated at the conservation both of summed electric charge and of any lepton number may serve as the first confirmation of a given theory, in which the mass, charge and vector moment of the neutrino proportionally respectively to the mass, charge and vector moment of lepton of the same family.