Hidden symmetries in two dimensional field theory

The bosonization process elegantly shows the equivalence of massless scalar and fermion fields in two space-time dimensions. However, with multiple fermions the technique often obscures global symmetries. Witten's non-Abelian bosonization makes these symmetries explicit, but at the expense of a somewhat complicated bosonic action. Frenkel and Kac have presented an intricate mathematical formalism relating the various approaches. Here I reduce these arguments to the simplest case of a single massless scalar field. In particular, using only elementary quantum field theory concepts, I expose a hidden $SU(2)\times SU(2)$ chiral symmetry in this trivial theory. I then discuss in what sense this field should be interpreted as a Goldstone boson.Comment: 15 pages. Revision adds numerous references and puts things in better historical contex

The Genetics of the Mood Disorder Spectrum: Genome-wide Association Analyses of More Than 185,000 Cases and 439,000 Controls

Background: Mood disorders (including major depressive disorder and bipolar disorder) affect 10% to 20% of the population. They range from brief, mild episodes to severe, incapacitating conditions that markedly impact lives. Multiple approaches have shown considerable sharing of risk factors across mood disorders despite their diagnostic distinction. / Methods: To clarify the shared molecular genetic basis of major depressive disorder and bipolar disorder and to highlight disorder-specific associations, we meta-analyzed data from the latest Psychiatric Genomics Consortium genome-wide association studies of major depression (including data from 23andMe) and bipolar disorder, and an additional major depressive disorder cohort from UK Biobank (total: 185,285 cases, 439,741 controls; nonoverlapping N = 609,424). / Results: Seventy-three loci reached genome-wide significance in the meta-analysis, including 15 that are novel for mood disorders. More loci from the Psychiatric Genomics Consortium analysis of major depression than from that for bipolar disorder reached genome-wide significance. Genetic correlations revealed that type 2 bipolar disorder correlates strongly with recurrent and single-episode major depressive disorder. Systems biology analyses highlight both similarities and differences between the mood disorders, particularly in the mouse brain cell types implicated by the expression patterns of associated genes. The mood disorders also differ in their genetic correlation with educational attainment—the relationship is positive in bipolar disorder but negative in major depressive disorder. / Conclusions: The mood disorders share several genetic associations, and genetic studies of major depressive disorder and bipolar disorder can be combined effectively to enable the discovery of variants not identified by studying either disorder alone. However, we demonstrate several differences between these disorders. Analyzing subtypes of major depressive disorder and bipolar disorder provides evidence for a genetic mood disorders spectrum

Extended Gauge Theories in Euclidean Space with Higher Spin Fields

The extended Yang-Mills gauge theory in Euclidean space is a renormalizable (by power counting) gauge theory describing a local interacting theory of scalar, vector, and tensor gauge fields (with maximum spin 2). In this article we study the quantum aspects and various generalizations of this model in Euclidean space. In particular the quantization of the pure gauge model in a common class of covariant gauges is performed. We generalize the pure gauge sector by including matter fermions in the adjoint representation of the gauge group and analyze its N=1 and N=2 supersymmetric extensions. We show that the maximum half-integer spin contained in these fermion fields in dimension 4 is 3/2. Moreover we develop an extension of this theory so as to include internal gauge symmetries and the coupling to bosonic matter fields. The spontaneous symmetry breaking of the extended gauge symmetry is also analyzed.Comment: LaTeX, 36 pages, section 4 expanded, new section 7 and new references added, to appear in Annals of Physic

Using baryon octet magnetic moments and masses to fix the pion cloud contribution

Using SU(3) symmetry to constrain the pion BB' couplings, assuming SU(3) breaking comes only from one-loop pion cloud contributions, and using the the covariant spectator theory to describe the photon coupling to the quark core, we show how the experimental masses and magnetic moments of the baryon octet can be used to set a model independent constraint on the strength of the pion cloud contributions to the octet, and hence the nucleon, form factors at Q2=0.Comment: 7 pages, 1 figur

Pairwise approach for analysis and reporting of child’s free sugars intake from a birth cohort study

Objectives: The prospective cohort design is an important research design, but a common challenge is missing data. The purpose of this study is to compare three approaches to managing missing data, the pairwise (n = 1386 children), the partial or modified pairwise (n = 1019) and the listwise (n = 546), to characterize the trajectories of children's free sugars intake (FSI) across early childhood. Methods: By applying the Group-based Trajectory Model Technique to three waves of data collected from a prospective cohort study of South Australian children, this study examined the three approaches in managing missing data to validate and discuss children's FSI trajectories. Results: Each approach identified three distinct trajectories of child's FSI from 1 to 5 years of age: (1) ‘low and fast increasing’, (2) ‘moderate and increasing’ and (3) ‘high and increasing’. The trajectory memberships were consistent across the three approaches, and were for the pairwise scenario (1) 15.1%, (2) 68.3% and (3) 16.6%; the partial or modified pairwise (1) 15.9%, (2) 64.1% and (3) 20.0%; and the listwise (1) 14.9%, (2) 64.9% and (3) 20.2% of children. Conclusions: Given the comparability of the findings across the analytical approaches and the samples' characteristics between baseline and across different data collection waves, it is recommended that the pairwise approach be used in future analyses to optimize the sample size and statistical power when examining the relationship between FSI in the first years of life and health outcome such as dental caries

Constraints, Histones, and the 30 Nanometer Spiral

We investigate the mechanical stability of a segment of DNA wrapped around a histone in the nucleosome configuration. The assumption underlying this investigation is that the proper model for this packaging arrangement is that of an elastic rod that is free to twist and that writhes subject to mechanical constraints. We find that the number of constraints required to stabilize the nuclesome configuration is determined by the length of the segment, the number of times the DNA wraps around the histone spool, and the specific constraints utilized. While it can be shown that four constraints suffice, in principle, to insure stability of the nucleosome, a proper choice must be made to guarantee the effectiveness of this minimal number. The optimal choice of constraints appears to bear a relation to the existence of a spiral ridge on the surface of the histone octamer. The particular configuration that we investigate is related to the 30 nanometer spiral, a higher-order organization of DNA in chromatin.Comment: ReVTeX, 15 pages, 18 figure

Effective field theory and the quark model

We analyze the connections between the quark model (QM) and the description of hadrons in the low-momentum limit of heavy-baryon effective field theory in QCD. By using a three-flavor-index representation for the effective baryon fields, we show that the ``nonrelativistic'' constituent QM for baryon masses and moments is completely equivalent through O(m_s) to a parametrization of the relativistic field theory in a general spin--flavor basis. The flavor and spin variables can be identified with those of effective valence quarks. Conversely, the spin-flavor description clarifies the structure and dynamical interpretation of the chiral expansion in effective field theory, and provides a direct connection between the field theory and the semirelativistic models for hadrons used in successful dynamical calculations. This allows dynamical information to be incorporated directly into the chiral expansion. We find, for example, that the striking success of the additive QM for baryon magnetic moments is a consequence of the relative smallness of the non-additive spin-dependent corrections.Comment: 25 pages, revtex, no figure

Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction

For a system of spinless one-dimensional fermions, the non-vanishing short-range limit of two-body interaction is shown to induce the wave-function discontinuity. We prove the equivalence of this fermionic system and the bosonic particle system with two-body $\delta$-function interaction with the reversed role of strong and weak couplings. KEYWORDS: one-dimensional system, $\epsilon$-interaction, solvable many-body problem, exact bosonizationComment: 4 pages ReVTeX 4 epsf figures included, new Ref

Vacuum orbit and spontaneous symmetry breaking in hyperbolic sigma models

We present a detailed study of quantized noncompact, nonlinear SO(1,N) sigma-models in arbitrary space-time dimensions D \geq 2, with the focus on issues of spontaneous symmetry breaking of boost and rotation elements of the symmetry group. The models are defined on a lattice both in terms of a transfer matrix and by an appropriately gauge-fixed Euclidean functional integral. The main results in all dimensions \geq 2 are: (i) On a finite lattice the systems have infinitely many nonnormalizable ground states transforming irreducibly under a nontrivial representation of SO(1,N); (ii) the SO(1,N) symmetry is spontaneously broken. For D =2 this shows that the systems evade the Mermin-Wagner theorem. In this case in addition: (iii) Ward identities for the Noether currents are derived to verify numerically the absence of explicit symmetry breaking; (iv) numerical results are presented for the two-point functions of the spin field and the Noether current as well as a new order parameter; (v) in a large N saddle-point analysis the dynamically generated squared mass is found to be negative and of order 1/(V \ln V) in the volume, the 0-component of the spin field diverges as \sqrt{\ln V}, while SO(1,N) invariant quantities remain finite.Comment: 60 pages, 12 Figures, AMS-Latex; v2: results on vacuum orbit and spontaneous symmetry breaking extended to all dimension