Lie algebra cohomology and group structure of gauge theories

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator $Q^{\dagger}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincar\'e duality - with respect to gauge anomalies and Wess-Zumino-Witten topological terms. We consider the consistent embedding of the BRST adjoint generator $Q^{\dagger}$ into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint N\"other charge $Q^{\dagger}$.Comment: 24 pages, RevTex, Revised version submitted to J. Math. Phy

Emergent Geometry and Quantum Gravity

We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale L_P. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of symplectic structure \omega in terms of electromagnetic fields F=dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.Comment: Invited Review for Mod. Phys. Lett. A, 17 page

Geodesic Motions in 2+1 Dimensional Charged Black Holes

We study the geodesic motions of a test particle around 2+1 dimensional charged black holes. We obtain a class of exact geodesic motions for the massless test particle when the ratio of its energy and angular momentum is given by square root of cosmological constant. The other geodesic motions for both massless and massive test particles are analyzed by use of numerical method.Comment: 13page

Quantitative Screening of Cervical Cancers for Low-Resource Settings: Pilot Study of Smartphone-Based Endoscopic Visual Inspection After Acetic Acid Using Machine Learning Techniques

Background: Approximately 90% of global cervical cancer (CC) is mostly found in low- and middle-income countries. In most cases, CC can be detected early through routine screening programs, including a cytology-based test. However, it is logistically difficult to offer this program in low-resource settings due to limited resources and infrastructure, and few trained experts. A visual inspection following the application of acetic acid (VIA) has been widely promoted and is routinely recommended as a viable form of CC screening in resource-constrained countries. Digital images of the cervix have been acquired during VIA procedure with better quality assurance and visualization, leading to higher diagnostic accuracy and reduction of the variability of detection rate. However, a colposcope is bulky, expensive, electricity-dependent, and needs routine maintenance, and to confirm the grade of abnormality through its images, a specialist must be present. Recently, smartphone-based imaging systems have made a significant impact on the practice of medicine by offering a cost-effective, rapid, and noninvasive method of evaluation. Furthermore, computer-aided analyses, including image processing-based methods and machine learning techniques, have also shown great potential for a high impact on medicinal evaluations

Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories

We derive maps relating the currents and energy-momentum tensors in noncommutative (NC) gauge theories with their commutative equivalents. Some uses of these maps are discussed. Especially, in NC electrodynamics, we obtain a generalization of the Lorentz force law. Also, the same map for anomalous currents relates the Adler-Bell-Jackiw type NC covariant anomaly with the standard commutative-theory anomaly. For the particular case of two dimensions, we discuss the implications of these maps for the Sugawara-type energy-momentum tensor.Comment: 14 pages, JHEP styl

Collective excitation of quantum wires and effect of spin-orbit coupling in the presence of a magnetic field along the wire

The band structure of a quantum wire with the Rashba spin-orbit coupling develops a pseudogap in the presence of a magnetic field along the wire. In such a system spin mixing at the Fermi wavevectors $-k_F$ and $k_F$ can be different. We have investigated theoretically the collective mode of this system, and found that the velocity of this collective excitation depends sensitively on the strength of the Rashba spin-orbit interaction and magnetic field. Our result suggests that the strength of the spin-orbit interaction can be determined from the measurement of the velocity.Comment: RevTeX 4 file, 4pages, 6 eps figures. To appear in Physical Review

X-ray edge problem of graphene

The X-ray edge problem of graphene with the Dirac fermion spectrum is studied. At half-filling the linear density of states suppresses the singular response of the Fermi liquid, while away from half-filling the singular features of the Fermi liquid reappear. The crossover behavior as a function of the Fermi energy is examined in detail. The exponent of the power-law absorption rate depends both on the intra- and inter-valley scattering, and it changes as a function of the Fermi energy, which may be tested experimentally.Comment: 7 pages, 1 figur

Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.