Rm Cr Research Articles

Dynamical Symmetry Breaking in QED3 from the Wilson RG Point of View

Dynamical symmetry breaking in three dimensional QED with $N$ flavors, which has been mostly analyzed by solving the Schwinger-Dyson equations, is investigated by means of the approximated Wilson, or non-perturbative, renormalization group (RG). We study the RG flows of the gauge coupling and the general four-fermi couplings allowed by the symmetry with concentrating our interest on study of the phase structure. The RG equations have no gauge parameter dependence in our approximation scheme. It is found that there exist chirally broken and unbroken phases for $N > N_{\rm cr}$ ($3 < N_{\rm cr} < 4$) and that the unbroken phase disappears for $N < N_{\rm cr}$. We also discuss the spontaneous parity breaking in three dimensional QED with the four-fermi interactions.

Photon Splitting and Pair Creation in Highly Magnetized Pulsars

The absence of radio pulsars with long periods has lead to the popular notion of a high P ``death line.'' In the standard picture, beyond this boundary, pulsars with low spin rates cannot accelerate particles above the stellar surface to high enough energies to initiate pair cascades, and the pair creation needed for radio emission is strongly suppressed. In this paper we explore the possibility of another pulsar ``death line'' in the context of polar cap models, corresponding to high magnetic fields B in the upper portion of the period-period derivative diagram, a domain where few radio pulsars are observed. The origin of this high B boundary, which may occur when B becomes comparable to or exceeds $B_{\rm cr} = 4.4 \times 10^{13}$ Gauss, is also due to the suppression of magnetic pair creation, but primarily because of ineffective competition with magnetic photon splitting. Threshold pair creation also plays a prominent role in the suppression of cascades. We present Monte Carlo calculations of the pair yields in photon splitting/pair cascades which show that, in the absence of scattering effects, pair production is effectively suppressed, but only if all three modes of photon splitting allowed by QED are operating in high fields. This paper describes the probable shape and position of the new ``death line,'' above which pulsars are expected to be radio quiet, but perhaps still X-ray and gamma-ray bright. The hypothesized existence of radio-quiet sources finds dramatic support in the recent discovery of ultra-strong fields in Soft Gamma-ray Repeaters and Anomalous X-ray Pulsars. Guidelines for moderate to high B pulsar searches at radio wavelengths and also in the soft and hard gamma-ray bands are presented.

On removable singularities for integrable cr functions

Let $M$ be a locally embeddable CR manifold. One defines, for $p\geq 1$, $$L^p_{\rm loc,CR}(M)=\{f\in L^p_{\rm loc}(M)| f {\rm is CR on} M\},$$ $$L^p_{\rm loc,CR}(M-E)=\{f\in L^p_{\rm loc}(M)| f {\rm is CR on} M-E\},$$ with $E$ a closed subset of $M$. This paper gives conditions under which $L^p_{\rm loc,CR}(M)=L^p_{\rm loc,CR}(M-E)$. In order to state results, let us recall the following definitions. Definition 1: The CR orbit of $p\in M$ is defined as $O_{\rm CR}(M,p)=\{q\in M|$ there exists a piecewise smooth integral curve of $T^cM$ with origin $p$ and target $q\}$. By Sussmann's theorem, $O_{\rm CR}(M,p)$ has the structure of a smooth immersed submanifold of $M$ [see M. S. Baouendi, P. Ebenfelt and L. P. Rothschild, Real submanifolds in complex space and their mappings, Princeton Univ. Press, Princeton, NJ, 1999; MR1668103 (2000b:32066)]. Definition 2: $M$ is globally minimal if $M$ is a single orbit. Let $H^k$ denote $k$-dimensional Hausdorff measure. The main general assumption throughout the paper is that $M$ and $M-E$ are globally minimal ($M$ globally minimal does not imply $M-E$ globally minimal). Among the results of the paper, we state the following theorem: Let $M$ be $C^{2,\alpha}, 0<\alpha<1$, of real dimension $d$ and CR dimension $\geq 1$. Let $E\subset M$ be a closed subset with $H^{d-3}(E)<\infty$. Assume that $M$ and $M-E$ are globally minimal. Then $L^p_{\rm loc,CR}(M)=L^p_{\rm loc,CR}(M-E)$.

Photon splitting in strong magnetic fields: Asymptotic approximation formulas versus accurate numerical results

We present the results of a numerical calculation of the photon splitting rate below the electron-pair creation threshold ($\omega \le 2m$) in magnetic fields $B ~{> \atop \sim}~ B_{\rm cr} = m^2 /e = 4.414 \times 10^{9}$ T. Our results confirm asymptotic approximations derived in the low-field ($B < B_{\rm cr}$) and high-field ($B \gg B_{\rm cr}$) limit, and allow interpolating between the two asymptotic regions. Our expression for the photon splitting rate is a simplified version of a formula given by Mentzel et al. We also point out that, although the analytical formula is correct, the splitting rates calculated there are wrong due to an error in the numerical calculations.

Dynamics of gravitating magnetic monopoles.

According to previous work on magnetic monopoles, static regular solutions are nonexistent if the vacuum expectation value of the Higgs field $\eta$ is larger than a critical value $\eta_{{\rm cr}}$, which is of the order of the Planck mass. In order to understand the properties of monopoles for $\eta>\eta_{{\rm cr}}$, we investigate their dynamics numerically. If $\eta$ is large enough ($\gg\eta_{{\rm cr}}$), a monopole expands exponentially and a wormhole structure appears around it, regardless of coupling constants and initial configuration. If $\eta$ is around $\eta_{{\rm cr}}$, there are three types of solutions, depending on coupling constants and initial configuration: a monopole either expands as stated above, collapses into a black hole, or comes to take a stable configuration.

Orientational ordering of a polymer chain in a strong dipole field. Tetrahedral lattice model

AbstractOrientational and conformational properties have been investigated of a rotational isomeric model of a polar polymer chain on a tetrahedral lattice in a strong electric or mechanical field of dipole symmetry. Two types of dipole moment distribution along the chain are discussed: (A) constant signs of longitudinal components of the dipole moments, and (B) alternating signs of the longitudinal components of the dipole moments. The second case represents polymer chains such as \documentclass{article}\pagestyle{empty}\begin{document}$ \rlap{--} ({\rm CH}_{\rm 2} \hbox{---} {\rm CR}_{\rm 2} {\rm \rlap{--} )}_n $\end{document}&gt;/UEQN&gt; when the dipole moments are oriented along the bisector of the CR2‐angle, i.e., normal to the extended trans‐chain conformation. It is shown that only a discrete most probable orientation of the lattice relative to the field should be considered, namely that coinciding with one of the symmetry axes of the lattices. The average dipole order parameter and dichroic functions (quadrupole order parameter) are calculated in a strong external dipole field for unit vectors with different orientation relative to the chain backbone. The quadrupole order parameter for different unit vectors is obtained also as a function of chain elongation. The polarizability induced by an additional weak dipole field is calculated as a function of the magnitude of the strong external dipole field. For the model considered here the order parameters are more strongly influenced by the external field than those for the freely jointed chain (FJC) model having the same distribution of dipole moments along the chain. The orientational ordering of the chain in a dipole field is higher than in a quadrupole field of the same magnitude.

Thirring Model as a Gauge Theory

We reformulate the Thirring model in $D$ $(2 \le D < 4)$ dimensions as a gauge theory by introducing $U(1)$ hidden local symmetry (HLS) and study the dynamical mass generation of the fermion through the Schwinger-Dyson (SD) equation. By virtue of such a gauge symmetry we can greatly simplify the analysis of the SD equation by taking the most appropriate gauge (``nonlocal gauge'') for the HLS. In the case of even-number of (2-component) fermions, we find the dynamical fermion mass generation as the second order phase transition at certain fermion number, which breaks the chiral symmetry but preserves the parity in (2+1) dimensions ($D=3$). In the infinite four-fermion coupling (massless gauge boson) limit in (2+1) dimensions, the result coincides with that of the (2+1)-dimensional QED, with the critical number of the 4-component fermion being $N_{\rm cr} = \frac{128}{3\pi^{2}}$. As to the case of odd-number (2-component) fermion in (2+1) dimensions, the regularization ambiguity on the induced Chern-Simons term may be resolved by specifying the regularization so as to preserve the HLS. Our method also applies to the (1+1) dimensions, the result being consistent with the exact solution. The bosonization mechanism in (1+1) dimensional Thirring model is also reproduced in the context of dual-transformed theory for the HLS.

Separation of spin and charge quantum numbers in strongly correlated systems.

In this paper we reexamine the problem of the separation of spin and charge degrees of freedom in two dimensional strongly correlated systems. We establish a set of sufficient conditions for the occurence of spin and charge separation. Specifically, we discuss this issue in the context of the Heisenberg model for spin-1/2 on a square lattice with nearest ($J_1$) and next-nearest ($J_2$) neighbor antiferromagnetic couplings. Our formulation makes explicit the existence of a local SU(2) gauge symmetry once the spin-1/2 operators are replaced by bound states of spinons. The mean-field theory for the spinons is solved numerically as a function of the ratio $J_2/J_1$ for the so-called s-RVB Ansatz. A second order phase transition exists into a novel flux state for $J_2/J_1>(J_2/J_1)_{{\rm cr}}$. We identify the range $0<J_2/J_1<(J_2/J_1)_{\rm cr}$ as the s-RVB phase. It is characterized by the existence of a finite gap to the elementary excitations (spinons) and the breakdown of all the continuous gauge symmetries. An effective continuum theory for the spinons and the gauge degrees of freedom is constructed just below the onset of the flux phase. We argue that this effective theory is consistent with the deconfinement of the spinons carrying the fundamental charge of the gauge group. We contrast this result with the study of the one dimensional quantum antiferromagnet within the same approach. We show that in the one dimensional model, the spinons of the gauge picture are always confined and thus cannot be identified with the gapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.

Radiation effects on poly(1‐chloro‐1‐alkynes)

AbstractThe γ‐radiolysis behavior of poly(l‐chloro‐1‐alkynes) \[ [\rlap{‐‐} ({\rm CCI} = {\rm CR}\rlap{‐‐} )_n ;{\rm R} = n ‐ {\rm alkyl}] \] greatly changed with the length of alkyl group and with the presence or absence of oxygen. When γ‐irradiated in air, poly(l‐chloro‐1‐hexyne) (R = n‐C4H9) decomposed to oligomers; its Gs value was as large as 5.4. When irradiated in vacuum, this polymer partly gelled. In contrast, poly(l‐chloro‐1‐decyne) (R = n‐C8H17) partly gelled even by irradiation in air. A high‐dose irradiation of this polymer in vacuum resulted in the quantitative formation of a gel. The polymers irradiated in air contained carbonyl and hydroxyl groups, indicating the participation of oxidation reaction. Comparison with their thermolysis leads to a conclusion that these Cl‐containing polyacetylenes are radiation‐sensitive irrespective of their high thermal stability.

Homocystinuria caused by 5,10-methylenetetrahydrofolate reductase deficiency: A case in an infant responding to methionine, folinic acid, pyridoxine, and vitamin B 12 therapy

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Dynamics of a conformational change in aqueous 18‐crown‐6 by an ultrasonic absorption method

AbstractA temperature dependence study of the ultrasonic amplitudes, velocities, and relaxation times for a presumed conformational transition of noncomplexed aqueous 18‐crown‐6 (1,4,7,10,13,16‐hexaoxacyclooctadecane) is discussed. At all temperatures a single relaxation was observed within a 15–255‐MHz frequency range. The equilibrium constant for the presumed conformational transition \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CR}_1 \mathop \rightleftarrows\limits^{K_{12} } {\rm CR}_2 $\end{document} was determined to be K21 = (2 ± 2) × 10−2. The activation parameters are ΔH21≠ = 10.2 ± 1.0 kcal/mol, ΔS21≠ = 7.7 ± 0.2 cal/(mol·deg), ΔH12≠ = 7.4 ± 1.0 kcal/mol, and ΔS12≠ = 7.7 ± 0.2 cal/(mol·deg), while the thermodynamic enthalpy and entropy were found to be −2.6 ± 1.0 kcal/mol and 0 ± 0.2 cal/(mol·deg), respectively. The rate constants at 25.0°C for the presumed conformational transition are k21 = (1.0 ± 0.3) × 107 sec−1 and k12 = (6.2 ± 0.2) × 108 sec−1.

Measurement of Blood Flow in the Mouse Tail after Irradiation

The measurement of the local clearance rate after subcutaneous injection of ${}^{133}{\rm Xe}$ and $[{}^{51}{\rm Cr}]{\rm EDTA}$ provided a way to obtain information on blood flow and capillary diffusion capacity (CDC) in the mouse tail. These studies were performed under normal resting conditions and after the induction of maximal blood flow. A decrease in blood flow and CDC was observed about a year after tail irradiation with a single dose of 3000 rad X rays. This decrease was most significant under maximal blood flow conditions. The dose-effect curves for single doses when measured at 14-17 mo after irradiation showed a decrease in blood flow up to 2500 rad; whereas, after doses higher than 2500 rad, an increase in blood flow was observed. The same phenomenon was observed with the CDC; however, it was less pronounced. Studies of blood flow and CDC after fractionated irradiations demonstrated no significantly different curves, if the doses were expressed in ret. This indicates that the Ellis formula is...