Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An explicit formula for the secular equations is given in term of a set of polynomials. The spectrum exhibits a fractal structure in the infinite volume limit. An exact result concerning the index theorem for the overlap Dirac operator is obtained.Comment: 8 pages, latex, 3 eps figures, minor correction

Gauge Equivalence in Two--Dimensional Gravity

Two-dimensional quantum gravity is identified as a second-class system which we convert into a first-class system via the Batalin-Fradkin (BF) procedure. Using the extended phase space method, we then formulate the theory in most general class of gauges. The conformal gauge action suggested by David, Distler and Kawai is derived from a first principle. We find a local, light-cone gauge action whose Becchi-Rouet-Stora-Tyutin invariance implies Polyakov's curvature equation $\partial_{-}R=\partial_{-}^{3}g_{++}=0$, revealing the origin of the $SL(2,R)$ Kac-Moody symmetry. The BF degree of freedom turns out be dynamically active as the Liouville mode in the conformal gauge, while in the light-cone gauge the conformal degree of freedom plays that r{\^o}le. The inclusion of the cosmological constant term in both gauges and the harmonic gauge-fixing are also considered.Comment: 30 pages, KANAZAWA 93-

Axial anomaly in the reduced model: Higher representations

The axial anomaly arising from the fermion sector of \U(N) or \SU(N) reduced model is studied under a certain restriction of gauge field configurations (the ``\U(1) embedding'' with $N=L^d$). We use the overlap-Dirac operator and consider how the anomaly changes as a function of a gauge-group representation of the fermion. A simple argument shows that the anomaly vanishes for an irreducible representation expressed by a Young tableau whose number of boxes is a multiple of $L^2$ (such as the adjoint representation) and for a tensor-product of them. We also evaluate the anomaly for general gauge-group representations in the large $N$ limit. The large $N$ limit exhibits expected algebraic properties as the axial anomaly. Nevertheless, when the gauge group is \SU(N), it does not have a structure such as the trace of a product of traceless gauge-group generators which is expected from the corresponding gauge field theory.Comment: 21 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in JHE

Batalin-Tyutin Quantization of the Self-Dual Massive Theory in Three Dimensions

We quantize the self-dual massive theory by using the Batalin-Tyutin Hamiltonian method, which systematically embeds second class constraint system into first class one in the extended phase space by introducing the new fields. Through this analysis we obtain simultaneously the St\"uckelberg scalar term related to the explicit gauge-breaking effect and the new type of Wess-Zumino action related to the Chern-Simons term.Comment: 17 pages, SOGANG-HEP 191/9

Charge dynamics in strongly correlated one-dimensional Cu-O chain systems revealed by inelastic X-ray scattering

We report on the Cu 1s resonant inelastic X-ray scattering (RIXS) of Cu-O one-dimensional (1D) strongly correlated insulator systems with contrasting atomic arrangements, namely edge-sharing CuGeO3 and corner-sharing Sr2CuO3. Owing to good statistics of the high-resolution RIXS data, so far unresolved fine structures are revealed. Detailed photon-energy and momentum dependence of the RIXS spectra in comparison with theoretical calculations has clarified the natures of the low-energy charge excitations and hybridization of the electronic states.Comment: 4 pages, 3 color figure

PGC-1α Is a Key Regulator of Glucose-Induced Proliferation and Migration in Vascular Smooth Muscle Cells

BACKGROUND: Atherosclerosis is a complex pathological condition caused by a number of mechanisms including the accelerated proliferation of vascular smooth muscle cells (VSMCs). Diabetes is likely to be an important risk factor for atherosclerosis, as hyperglycemia induces vascular smooth muscle cell (VSMC) proliferation and migration and may thus contribute to the formation of atherosclerotic lesions. This study was performed to investigate whether PGC-1alpha, a PPARgamma coactivator and metabolic master regulator, plays a role in regulating VSMC proliferation and migration induced by high glucose. METHODOLOGY/PRINCIPAL FINDINGS: PGC-1alpha mRNA levels are decreased in blood vessel media of STZ-treated diabetic rats. In cultured rat VSMCs, high glucose dose-dependently inhibits PGC-1alpha mRNA expression. Overexpression of PGC-1alpha either by infection with adenovirus, or by stimulation with palmitic acid, significantly reduces high glucose-induced VSMC proliferation and migration. In contrast, suppression of PGC-1alpha by siRNA mimics the effects of glucose on VSMCs. Finally, mechanistic studies suggest that PGC-1alpha-mediated inhibition of VSMC proliferation and migration is regulated through preventing ERK1/2 phosphorylation. CONCLUSIONS/SIGNIFICANCE: These results indicate that PGC-1alpha is a key regulator of high glucose-induced proliferation and migration in VSMCs, and suggest that elevation of PGC-1alpha in VSMC could be a useful strategy in preventing the development of diabetic atherosclerosis

The provocative lumbar facet joint

Low back pain is the most common pain symptom experienced by American adults and is the second most common reason for primary care physician visits. There are many structures in the lumbar spine that can serve as pain generators and often the etiology of low back pain is multifactorial. However, the facet joint has been increasingly recognized as an important cause of low back pain. Facet joint pain can be diagnosed with local anesthetic blocks of the medial branches or of the facet joints themselves. Subsequent radiofrequency lesioning of the medial branches can provide more long-term pain relief. Despite some of the pitfalls associated with facet joint blocks, they have been shown to be valid, safe, and reliable as a diagnostic tool. Medial branch denervation has shown some promise for the sustained control of lumbar facet joint-mediated pain, but at this time, there is insufficient evidence that it is a wholly efficacious treatment option. Developing a universal algorithm for evaluating facet joint-mediated pain and standard procedural techniques may facilitate the performance of larger outcome studies. This review article provides an overview of the anatomy, pathophysiology, diagnosis, and treatment of facet joint-mediated pain