Differential Forms and the Noncommutative Residue for Manifolds with Boundary in the Non-product Case

In this Letter, for an even-dimensional compact manifold with boundary which has the non-product metric near the boundary, we use the noncommutative residue to define a conformal invariant pair. For a four-dimensional manifold, we compute this conformal invariant pair under some conditions and point out the way of computations in the general.     

Wigner Function for Klein-Gordon Landau Problem

First we calculate the Wigner phase-space distribution function for the Klein-Gordan Landau problem on a commmutative space. Then we study the modifications introduced by the coordinate-coordinate noncommuting and momentum-momentum noncommuting, namely, by using a generalized Bopp＇s shift method we construct the Wigner function for the Klein-Gordan Landau problem both on a noncommutative space （NCS） and a noncommutative phase space （NCPS）.     

Noncommutative geometric spaces with boundary: Spectral action

We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the hermiticity of the Dirac operator. We then define spectral triples of noncommutative spaces with boundary. In particular we evaluate the spectral action corresponding to the noncommutative space of the standard model and show that the Einstein–Hilbert action gets modified by the addition of the extrinsic curvature terms with the right sign and coefficient necessary for consistency of the Hamiltonian. We also include effects due to the addition of a dilaton field.     

A New Type of Seiberg-Witten Map and Its Application

Deformation quantization is a powerful tool to deal with systems in noncommutative space to get their energy spectra and corresponding Wigner functions, especially for the ease of both coordinates and momenta being noneommutative. In order to simplify solutions of the relevant .-genvalue equation, we introduce a new kind of Seiberg Witten-like map to change the variables of the noncommutative phase space into ones of a commutative phase space, and demonstrate its role via an example of two-dimensional oscillator with both kinetic and elastic couplings in the noneommutative phase space.     

Noncommutative Inspired Reissner-Nordstrom Black Holes in Large Extra Dimensions

Recently, a new noncommutative geometry inspired solution of the coupled Einstein Maxwell field equations including black holes in 4-dimension is found. In this paper, we generalize some aspects of this model to the Reissner Nordstrom （RN） like geometries with large extra dimensions. We discuss Hawking radiation process based on noncommutative inspired solutions. In this framework, existence of black hole remnant and possibility of its detection in LHC are investigated.     

Parikh-Wilczek Tunneling as Massive Particles from Noncommutative Schwarzschild Black Hole

In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the thermodynamical relations in black hole. We calculate the emission rate of the massive particles＇ tunneling from a Schwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noneommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.     

Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time

The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutative space-time, a modified propagator and free energy are derived by means of functional integrals method. Moreover, quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.     

Drinfeld-Manin instanton and its noncommutative generalization

The Drinfeld-Manin construction of U（N） instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U（N） （N ≥ 2k - 1） k-instantons. For the N 〈 2k - 1 case, implicit results are given systematically as further constraints. We find that this formulism can easily be generalized to the noncommutative case, where the explicit solutions are also obtained.     

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall （QH） effect on a noncommutative phase space （NCPS）. By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and θ^-, respectively. In our calculation, we assume that these parameters vary from laver to laver.     

Noncommutative Singular Black Holes

In this paper, applying the method of coordinate coherent states to describe a noncommutative model of Vaidya black holes leads to an exact （t - r） dependence of solution in terms of the noncommutative parameter σ. In this setup, there Js no black hole remnant at long times.     

Decomposition of Noncommutative U（1） Gauge Potential

We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor     

Effective Action for Noncommutative U（1） Gauge Theory with Higher Dimensional Terms

In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously from a scale ANC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U（1） gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.     

DKP Oscillator in a Noncommutative Space

We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter.     

Lower-Dimensional Volumes and Kastler-Kalau-Walze Type Theorem for Manifolds with Boundary

In this paper, we define lower-dimensional volumes of spin manifolds with boundary. We compute the lower-dimensional volume Vol^(2,2) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also get the Kastler-Kalau-Walze type theorem in this case.     

Effects of N/Z on Spin Distribution of Evaporation Residue Cross Section as a Probe of Nuclear Dissipation

The spin distribution of the evaporation residue cross section of nuclei ^194pb, ^200Pb, ^206Pb, and ^200 Os are calculated via a Langevin equation coupled with a statistical decay model. It is shown that with increasing the neutronto-proton ratio （N/Z） of the system, the sensitivity of the significantly. Moreover, for ^200Os this spin distribution is no spin distribution to the nuclear dissipation is decreased longer sensitive to the nuclear dissipation. These results suggest that to obtain a more accurate pre-saddle viscosity coefficient through the measurement of the evaporation residue spin distribution, it is best to yield those compound systems with low N/Z.     

Roles of Isospin in Evaporation Residue Cross Section as a Probe of Nuclear Dissipation

The influence of isospin on the excess of evaporation residue cross section over its standard statistical-model value for nuclei ^194pb, ^200Pb, and ^206pb is studied via a Langevin equation coupled with a statistical decay model. The magnitude of this excess for a low-isospin fissioning nucleus is shown to be larger and its dependence on the nuclear viscosity coefficient to be stronger than those of a high-isospin fissioning nucleus. These results suggest that to obtain a more accurate information of viscosity coefficient inside the saddle point by measuring evaporation residue cross sections, we had better choose those compound systems with small isospin.     

Volumes of compact manifolds

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some parameters, set up a metric, which induces a volume element, and perform the integration for the adequate range of the parameters; in most cases our manifolds will be either spheres or (twisted) products of spheres, or quotients of spheres (homogeneous spaces).Our results should be useful in several physical instances, as instanton calculations, propagators in curved spaces, sigma models, geometric scattering in homogeneous manifolds, density matrices for entangled states, etc. Some flag manifolds have also appeared recently as exceptional holonomy manifolds; the volumes of compact Einstein manifolds appear in string theory.     

Einstein Gravity in Almost Kähler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics

We argue that the Einstein gravity theory can be reformulated in almost Kähler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation on manifolds enabled with nonholonomic distributions is considered. We prove that, for certain types of nonholonomic constraints, there are modelled effective Lagrangians which do not develop instabilities. It is also elaborated a linearization formalism for anholonomic noncommutative gravity theories models and analyzed the stability of stationary ellipsoidal solutions defining some nonholonomic and/or nonsymmetric deformations of the Schwarzschild metric. We show how to construct nonholonomic distributions which remove instabilities in nonsymmetric gravity theories. It is concluded that instabilities do not consist a general feature of theories of gravity with nonsymmetric metrics but a particular property of some models and/or unconstrained solutions.     

Quaternionic complexes

Each regular or semi-regular integral affine orbit of the Weyl group of gl(2n + 2, ) invariantly determines a locally exact differential complex on a 4n dimensional quaternionic manifold. This gives quaternionic analogues of Dolbeault cohomology on complex manifolds. We compute the index of such complexes in the hyper-Kähler case, showing that quaternionic cohomology is not trivial.     

On noncommutative and pseudo-Riemannian geometry

We introduce the notion of a pseudo-Riemannian spectral triple which generalizes the notion of spectral triple and allows for a treatment of pseudo-Riemannian manifolds within a noncommutative setting. It turns out that the relevant spaces in noncommutative pseudo-Riemannian geometry are not Hilbert spaces any more but Krein spaces, and Dirac operators are Krein-selfadjoint. We show that the noncommutative tori can be endowed with a pseudo-Riemannian structure in this way. For the noncommutative tori as well as for pseudo-Riemannian spin manifolds the dimension, the signature of the metric, and the integral of a function can be recovered from the spectral data.