Bulletin of the American Physical Society
2007 APS April Meeting
Volume 52, Number 3
Saturday–Tuesday, April 14–17, 2007; Jacksonville, Florida
Session M14: Theory II |
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Sponsoring Units: DPF Chair: Scott Yost, Baylor University Room: Hyatt Regency Jacksonville Riverfront City Terrace 10 |
Sunday, April 15, 2007 3:15PM - 3:27PM |
M14.00001: Dirac Equation in Adjoint Representation and Co-adjoint Gauge Theory James Crawford In the standard model, the Clifford algebra generators in the Dirac equation are taken to be any 4x4 irreducible matrix representation. The generations of particles (each composed of two leptons and two quarks) and the electroweak gauge group (U(1)xSU(2)) are introduced ad hoc. The adjoint and co-adjoint representations of the Clifford algebra are each composed of 16x16 matrices, and these sets are mutually commuting, so neither representation is irreducible, but they form an irreducible set, since only one representation can be brought into block diagonal form (four 4x4 blocks). Consequently, if the adjoint representation is used in the Dirac equation we have four Dirac spinor fields, and the theory exhibits the full gauge invariance generated by the co-adjoint representation, U(2,2), since these representations commute. We discuss the possibility of obtaining the electroweak sector of the standard model in this way. [Preview Abstract] |
Sunday, April 15, 2007 3:27PM - 3:39PM |
M14.00002: Alternate Lorentz Transformations of Spacetime Coordinates and Maxwell and Dirac Fields Rollin S. Armour, Jr., Jose L. Balduz, Jr. Spacetime coordinates may transform under any one of five representations of the Lorentz group and yield well-defined Lorentz transformations for the Maxwell and Dirac fields. These reps are (1/2,1/2), (0,0)+(0,1), (0,0)+(1,0), (1/2,0)+(1/2,0), and (0,1/2)+(0,1/2). Doubling the usual four-component Dirac field into eight components, the Maxwell field and this doubled Dirac field transform under at least two shared rules in each of these five spacetimes. In four-vector spacetime, we find a spin-1/2 Maxwell field and a spin-1 eight-component Dirac field. These two have a Lagrangian density and a set of Minkowski-signature invariants common to all of their Lorentz transformations across all five spacetimes. We discuss the sixteen possible coordinate and field transformations for these two fields, and the five possibilities for the four-component Dirac field, leaving their respective equations covariant under the Lorentz group. [Preview Abstract] |
Sunday, April 15, 2007 3:39PM - 3:51PM |
M14.00003: ABSTRACT HAS BEEN MOVED TO Y11.00008 |
Sunday, April 15, 2007 3:51PM - 4:03PM |
M14.00004: All order epsilon-expansion of Gauss hypergeometric functions with integer and half-integer values of parameters Scott A. Yost, Mikhail Kalmykov, B.F.L. Ward We discuss a proof that the Laurent expansions of certain classes of Gauss hypergeometric functions are expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with polynomial coefficients. An efficient algorithm for the calculation of the higher-order coefficients of Laurent expansion is constructed. Some particular cases of Gauss hypergeometric functions are also discussed. [Preview Abstract] |
Sunday, April 15, 2007 4:03PM - 4:15PM |
M14.00005: Basic-Particle Formation Scheme \&Experimental Tests J.X. Zheng-Johansson, P.-I. Johansson Based on overall experimental observations, especially the pair processes, we have since several years proposed that a basic particle like the electron, proton, etc. is formed of an oscillatory elementary charge of zero rest mass (a vaculeon), and the resulting electromagnetic waves in a dielectric vacuum. The charge and its total kinetic energy endowed at creation are the two sole inputs. The remaining particle properties and their relations are given by the classical-mechanics solutions. In this way we have predicted among others particle's total energy, mass, Einstein mass-energy relation, relativistic energy- momentum relation, de Broglie wave and parameters, Schr\"odinger/Dirac equations (incl. nonlinear terms), and Newton's gravity, in overall agreement with observations, the descriptions by the Standard Model, and the basic laws of classical, quantum and relativistic mechanics. Also, the model vacuum contains an enormous ``dark energy'' of much current interest. There appears to exist no known indications that contradict the proposed scheme. It seems to take yet ingenuous designs for measuring the yet not observables to directly verify, or else falsify, the scheme. \ Refs: JXZJ \& PIJ in {\it Unif. of Clas., Quant. \& Rel. Mech. \& Four Forces}, Nova Sci. 2005, Fwd R Lundin; Quant. Theory \& Symm. IV, ed V Dobrev, Heron Press, 2006, 763; 771 (with RL); Prog. in Phys. {\bf 4}, 32, 2006; Phys. Essays, { \bf 19}, Nr.4, 2006; refs therein. [Preview Abstract] |
Sunday, April 15, 2007 4:15PM - 4:27PM |
M14.00006: The PEP electron R.L. Collins The main problem in finding a PEP (purely electromagnetic) model is, how to make charge using only solenoidal EM fields? A model has been found that creates an inverse square vxB field that mimics the E field from a charge. To see this, spin a skinny loop of B about a vertical diameter: the vxB field on one side points inwards and on the other outwards. Gauss' law finds no net charge. Now translate the spin axis to the left edge. vxB is twice as large on right, and zero on left. Gauss' law finds a net charge within, the sign depending on the direction of spin. This can be expanded to describe a spinning magnetic dipole. The PEP electron oscillates between configurations of a magnetic dipole and a toroidal E field, at the Compton frequency mc2/h. Flux is quantized, ensuring stability. In integral form, Gauss' law finds charge. But divergence vxB is zero, on average. What, no charge density? This enigma arises because charge is a mathematical construct, and is not a real substance. What is the size of an electron? Size conventionally means the part that contains charge. When measured by Coulomb scattering, the electron is a point particle, without size,. Despite this, the EM structure itself is very large, the vxB fields extending to infinity. The size can be zero or infinity, according what one measures. More at arxiv/physics/0611266. [Preview Abstract] |
Sunday, April 15, 2007 4:27PM - 4:39PM |
M14.00007: Fractional dynamics and the TeV regime of field theory Ervin Goldfain The description of complex dynamics in the TeV regime of field theory warrants the transition from ordinary calculus on smooth manifolds to fractional differentiation and integration. Starting from the principle of local scale invariance, we explore the spectrum of phenomena that is likely to emerge beyond the energy range of the standard model. We find that, in the deep ultraviolet region of field theory, a) fractional dynamics in Minkowski space-time is equivalent to field theory in curved space-time. This result points out to a natural integration of classical gravity in the framework of TeV physics; b) the three gauge groups of the standard model are rooted in the topological concept of fractional dimension. This result suggests that gauge bosons and fermions are unified through a fundamentally different mechanism than the one advocated by supersymmetry; c) fractional dynamics is the underlying source of parity violation in weak interactions and of the breaking of time-reversal invariance in processes involving neutral kaons. \underline {Note}: this work is available at doi:10.1016/j.cnsns.2006.06.001 [Preview Abstract] |
Sunday, April 15, 2007 4:39PM - 4:51PM |
M14.00008: Matter Described by Fractional Dimension Interactions Charles Chase, Laurence Bloxham, James Gimzewski, Makos Karageorgis We propose an alternate unified theory of matter, space, and time that is based upon the propagation, interaction, and dynamic equilibrium of a difference between systems that evolves at a fractional rate, generating a fractal space and time. A simplified fractional Lagrangian evolution operator is used to develop dynamically bound correlated systems of changing differences. We develop a master equation whose solutions describe the interaction and rate of change of correlated difference systems in terms of the fundamental units of momentum and a waiting interval as they change through correlated time intervals. Degrees of symmetry freedom occur from consideration of the number of difference systems interacting in a bound, correlated dynamic equilibrium. We apply the theory to gravitational and inertial force through variations in the waiting interval. [Preview Abstract] |
Sunday, April 15, 2007 4:51PM - 5:03PM |
M14.00009: A New invariant ds=ds$_{t}$+ds$_{\phi}$ in the String Theory Action Leads to Replacing The General Covariance In the SM Dirac Equation Gauge Derivatives With An Equivalent General Covariance In The Metric That This Dirac Equation is Derived From Joel Maker Substituting the invariant ds=ds$_{t}$+ds$_{\phi }$ into the string theory action gives a cross term 2ds$_{t}$ds$_{\phi }$ (ds was squared in finding the string theory action area) implying spin thus requiring linearization of a diagonized ds$^{2}$. Here ds$_{t}=\surd $g$_{oo}$dt This linearization replaces ds=ds$_{t}$+ds$_{\phi }$ with a matrix ds=$\alpha _{t}$ds$_{t}+\alpha _{\phi }$ds$_{\phi }$ and thereby replaces the general covariance in the gauge derivatives in the Standard Model (SM) with a general covariance in the\textit{ original} metric (given that ds$_{t}=\surd $g$_{oo}$dt) that is used to start the derivation of the SM Dirac equation. This puts in the general covariance at the very beginning of the Dirac equation derivation, \textit{where it belongs}. The result is a new Dirac equation ($\surd $\textbf{\textit{g}}$_{\mu \mu }$\textit{$\gamma $}$_{\mu }$\textit{$\partial \psi $/$\partial $x}$_{\mu }$\textit{+i$\omega \psi $=0 }with\textbf{~}\textbf{g}$_{oo}$=1-2e$^{2}$/rm$_{e}$c$^{2}$=1-r$_{H}$/r) that does not require the covariant gauge derivatives anymore but yet still \textit{retains }the general covariance creating a \textbf{ONE} free parameter theory, instead of 18 of the SM. For example this new Dirac equation has a singularity-stability radius r$_{H}$ and, because of equivalence principle considerations, is allowed only \textit{one} type of charge e. Thus near r$_{H}$ the 2P$_{3/2}$ state for this new Dirac equation gives a $\psi ^{tt}\psi $ azimuthal trifolium, 3 lobe shape; so this ONE charge e (so don't need \textbf{ color} to guarantee this) spends \textbf{1/3} of its time in each lobe (\textbf{fractionally charged} lobes), the lobe structure is locked into the center of mass \textbf{(asymptotic freedom}), there are\textbf{ six} 2P states (corresponding to the 6 flavors) ;~ which are the~~\textbf{main properties of quarks}!~ Thus we end up with the experimental implications of the Standard Model (SM) by postulating just ONE particle with mass and string theory finally then exchanges its excessive generality for a Ockam's razor optimized theory. [Preview Abstract] |
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