Session Z26: General Theory / Computational Physics II

Corrections to the geometrical interpretation of bosonization

Bosonization is a powerful approach for understanding certain strongly-correlated fermion systems, especially in one spatial dimension but also in higher dimensions\footnote{A.Houghton, H.-J. Kwon and J. B. Marston, Adv. in Phys. { \bf 49}, 141 (2000).}. The method may be interpreted geometrically in terms of deformations of the Fermi surface, and the quantum operator that effects the deformations may be expressed in terms of a bilinear combination of fermion creation and annihilation operators. Alternatively the deformation operator has an approximate representation in terms of coherent states of bosonic fields\footnote{A. H. Castro Neto and E. Fradkin, Phys. Rev. B {\bf 49}, 10877 (1994).}. Calculation of the inner product of deformed Fermi surfaces within the two representations reveals corrections to the bosonic picture both in one and higher spatial dimensions. We discuss the implications of the corrections for efforts to improve the usefulness of multidimensional bosonization.   

Emergent Anyons in Exactly Solvable Discrete Models for Topological Phases in Two Dimensions

Anyons can emerge as collective excitations in models of topological phases. Exactly solvable discrete models that describe two-dimensional topological phases were proposed by Kitaev, and Levin and Wen respectively. I will present the explicit form of the operators that create and move fluxons (anyonic quasiparticles living at the plaquettes) in the Levin-Wen models. The exchange and exclusion statistics of these fluxons are studied. In particular, I will discuss the topological properties of Fibonacci anyons emerging in a particular Levin-Wen model.   

Uniform Approximation from Symbol Calculus on a Spherical Phase Space

We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a uniform approximation of the $6j$-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area preserving, map between two pairs of intersecting level sets on the spherical phase space.   

Searching for B-modes with QUIET: Latest results from the maximum-likelihood pipeline

The polarisation of the cosmic microwave background (CMB) gives us unique information about the existence of primordial gravitational waves and the energy scale of inflation. QUIET is a ground-based CMB polarisation experiment, taking advantage of the world's most sensitive microwave radiometers, to search for B-modes in the CMB polarisation. The pilot phase data taking was finished in December 2010, consisting of around 250 000 diode hours of Q-band data at 43 GHz and about ten times more W-band data at 94 GHz. The data are analyzed by two independent pipelines, the maximum-likelihood (ML) pipeline and the pseudo-$C_\ell$ (PCl) pipeline. I will present the ML pipeline and our latest results.   

The Fourth Dimension and Transaction Line

The fourth dimension is basically the depth between two objects or the depth between an object. It is the z compared to the length, width, height. When one looks at a few objects the depth in between them is the fourth dimension. The transaction line is a relationship between two objects that are falling. This line allows the relationship to form so that they fall at the same time, regardless how much they weigh.   

Reconsidering Dark Matter

There is a difference between (a) distances of remote standard candles, SN Type Ia, and (b) distances based upon their red shifts. It was believed that these galaxies had accelerated and used Dark Energy. There are 2 assumptions not supported by observations. The first is that the red shifts for remote galaxies are due to the Doppler Effect associated with receding velocity. Hubble only observed red shifts as a function of distances of known stars, and never measured receding velocities. He suggested the Doppler Effect as a cause, but expressed doubt about the suggestion. There are other causes for a red shift - gravity red shift of light from the sun, and loss of photon energy by gravity interaction of photons with dust and gas in interstellar space. The second assumption is that Hubble's linear relationship between the observed red shift and the distance will be valid at very large distances. Increasing red shift corresponds to a decrease of photon energy towards zero, and cannot be used for very remote stars - where the photon energy approaches zero and the red shift dependence becomes nonlinear and asymptotic to a constant value. This predicts the difference between the galaxy distances and the distances determined from their observed red shifts. The recent Nobel Prize (to Schmidt, Reis, and Perlmutter) needs reexamination. Two basic assumptions that are the foundation of their work may not be accurate. Details are in my earlier essays in ``The Misunderstood Universe'', {\copyright} 2009. .   

The Exact Solution of The Pioneer Anomaly According to The General Theory of Relativity and The Hubble's Law

Radio metric data from Pioneer 10/11 indicate an apparent anomalous, constant, acceleration acting on the spacecraft with a magnitude $\sim 8 \times 10^{-10}$ m/s$^2$, directed towards the Sun[1,2]. Turyshev [7] examined the constancy and direction of the Pioneer anomaly, and concluded that the data a temporally decaying anomalous acceleration $-2 \times 10^{-11} \frac{m}{s^2 yr}$ with an over 10{\%} improvement in the residuals compared to a constant acceleration model. Anderson, who is retired from NASA's Jet Propulsion Laboratory (JPL), is that study's first author. He finds, so ``it's either new physics or old physics we haven't discovered yet.'' New physics could be a variation on Newton's laws, whereas an example of as-yet-to-be- discovered old physics would be a cloud of dark matter trapped around the sun[12]. In this paper I introduce the exact solution for the Pioneer anomaly depending on the general theory of relativity and the Hubble's law. According to my solution, there are two terms of decelerations that controls the Pioneer anomaly. The first is produced by moving the Pioneer spacecraft through the gravitational field of the Sun, which causes the velocity of the spacecraft to be decreased according to the Schwarzschild Geometry of freely infalling particle. This deceleration is responsible for varying behaviour of the Pioneer anomaly in Turyshev [7], depending on $1/r^{2.5}$ the distance from the sun. The second term is produced by the attractive force of the dark matter which is constant and equals to the Hubble's constant multiplied by the speed of light in vacuum.