Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions

We show that noncommutative gauge theory in two dimensions is an exactly solvable model. A cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a sum over contributions from classical solutions. We derive an explicit formula for the partition function of Yang-Mills theory defined on a projective module for an arbitrary noncommutativity parameter which is manifestly invariant under gauge Morita equivalence. The energy observables are shown to be smooth functions of . The construction of noncommutative instanton contributions to the path integral is described in some detail. In general, there are infinitely many gauge inequivalent contributions of fixed topological charge, along with a finite number of quantum fluctuations about each instanton. The associated moduli spaces are combinations of symmetric products of an ordinary two-torus whose orbifold singularities are not resolved by noncommutativity. In particular, the weak coupling limit of the gauge theory is independent of and computes the symplectic volume of the moduli space of constant curvature connections on the noncommutative torus.     

Measurement of persistence in 1D diffusion

Using a novel NMR scheme we observed persistence in 1D gas diffusion. Analytical approximations and numerical simulations have indicated that for an initially random array of spins undergoing diffusion, the probability p(t) that the average spin magnetization in a given region has not changed sign (i.e., "persists") up to time t follows a power law t(-straight theta), where straight theta depends on the dimensionality of the system. Using laser-polarized 129Xe gas, we prepared an initial "quasirandom" 1D array of spin magnetization and then monitored the ensemble's evolution due to diffusion using real-time NMR imaging. Our measurements are consistent with analytical and numerical predictions of straight theta approximately 0.12.     

<Emphasis Type="Italic">SL(2; R)</Emphasis> Duality of the Noncommutative DBI Lagrangian

We study the action of the SL(2; R) group on the noncommutative DBI Lagrangian. The symmetry conditions of this theory under the above group will be obtained. These conditions determine the extra U(1) gauge field. By introducing some consistent relations we observe that the noncommutative (or ordinary) DBI Lagrangian and its SL(2; R) dual theory are dual of each other. Therefore, we find some SL(2; R) invariant equations. In this case the noncommutativity parameter, its T -dual and its SL(2; R) dual versions are expressed in terms of each other. Furthermore, we show that on the effective variables, T -duality and SL(2; R) duality do not commute. We also study the effects of the SL(2; R) group on the noncommutative Chern–Simons action.     

Morita Base Change in Hopf-Cyclic (Co)Homology

In this paper, we establish the invariance of cyclic (co)homology of left Hopf algebroids under the change of Morita equivalent base algebras. The classical result on Morita invariance for cyclic homology of associative algebras appears as a special example of this theory. In our main application we consider the Morita equivalence between the algebra of complex-valued smooth functions on the classical 2-torus and the coordinate algebra of the noncommutative 2-torus with rational parameter. We then construct a Morita base change left Hopf algebroid over this noncommutative 2-torus and show that its cyclic (co)homology can be computed by means of the homology of the Lie algebroid of vector fields on the classical 2-torus.     

Conformally invariant fractals and potential theory

The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is solved in two dimensions. The dimension &fcirc;(straight theta) of the boundary set with local wedge angle straight theta is &fcirc;(straight theta) = pi / straight theta-25-c / 12 (pi-straight theta)(2) / straight theta(2pi-straight theta), with c the central charge of the model. As a corollary, the dimensions D(EP) of the external perimeter and D(H) of the hull of a Potts cluster obey the duality equation (D(EP)-1) (D(H)-1) = 1 / 4. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.     

Amplitudes with different helicity configurations of noncommutative QED

The amplitudes of purely photon processes of noncommutative QED (NCQED) are derived for different helicity configurations of photons. The basic ingredient is the NCQED counterpart of the Yang–Mills recursion relations by means of Berends and Giele. The explicit solutions of recursion relations for NCQED photon current with special helicity configurations and also recursion relations for the NCQED fermion–photon current with special helicity configurations of photons (all photons have plus helicity) are presented.     

Comments on the Morita equivalence

It is known that the noncommutative Yang-Mills (YM) theory with periodical boundary conditions on a torus at a rational noncommutativity parameter value is Morita equivalent to the ordinary YM theory with twisted boundary conditions on a dual torus. We give a simple derivation of this fact. We describe the one-to-one correspondence between these two theories and the corresponding gauge invariant observables. In particular, we show that under the Morita map, the Polyakov loops in the ordinary YM theory are converted to the open noncommutative Wilson loops discovered by Ishibashi, Iso, Kawai, and Kitazawa.     

Mikheyev-smirnov-wolfenstein effects in vacuum oscillations

We point out that for solar neutrino oscillations with the mass-squared difference of Deltam(2) approximately 10(-10)-10(-9) eV(2), i.e., in the so-called vacuum oscillation range, the solar matter effects are non-negligible, particularly for the low energy pp neutrinos. One consequence of this is that the values of the mixing angle straight theta and pi/2-straight theta are not equivalent, making it necessary to consider the entire physical range of the mixing angle 0相似文献   

Quantum electrodynamics with arbitrary charge on a noncommutative space

Using the Seiberg-Witten map, we obtain a quantum electrodynamics on a noncommutative space, which has arbitrary charge and keep the gauge invariance to at the leading order in theta. The one-loop divergence and Compton scattering are reinvestigated. The noncommutative effects are larger than those in ordinary noncommutative quantum electrodynamics.     

Passive scalar intermittency in low temperature helium flows

We report new measurements of mixing of passive temperature field in a turbulent flow. The use of low temperature helium gas allows us to span a range of microscale Reynolds number, R(lambda), from 100 to 650. The exponents xi(n) of the temperature structure functions approximately r(xi(n)) are shown to saturate to xi(infinity) approximately 1.45+/-0.1 for the highest orders, n approximately 10. This saturation is a signature of statistics dominated by frontlike structures, the cliffs. Statistics of the cliffs' characteristics are performed, particularly their widths are shown to scale as the Kolmogorov length scale.     

Supergravity,R invariance and spontaneous supersymmetry breaking

We show that in order for a U(1) gauge theory with a Fayet-Illiopoulos term to be consistently coupled to supergravity, preserving gauge invariance, the superpotential must be R invariant. A supersymmetric cosmological term and therefore an explicit mass-like term for the gravitino is forbidden by gauge invariance. This result severely constrains the possible models for non-gravitational interactions. We comment on possible mass term the gauginos induced by gravitational effects.     

Quantum electrodynamics with arbitrary charge on a noncommutative space

Using the Seiberg-Witten map,we obtain a quantum electrodynamics on a noncommutative space,which has arbitrary charge and keep the gauge invariance to at the leading order in theta.The one-loop divergence and Compton scattering are reinvestigated.The uoncommutative effects are larger than those in ordinary noncommutative quantum electrodynamics.     

Deviations from linear theory for fluctuations below the supercritical primary bifurcation to electroconvection

Over two decades ago it was predicted that nonlinear interactions between thermally driven fluctuations in dissipative nonlinear nonequilibrium systems lead to deviations from mean-field theory. Here we report experimental observations of such deviations as a supercritical primary bifurcation is approached. We measured the mean-square director-angle fluctuations below the bifurcation to electroconvection of two different nematic liquid crystals. For epsilon(mf) identical withV2/V(2)(c,mf)-1 less, similar-0.1 ( V is the applied voltage) we find approximately |epsilon(mf)|(-gamma) with gamma given by linear theory (LT). Closer to the bifurcation there are deviations from LT with a smaller gamma and with V(2)(c)>V(2)(c,mf).     

Theta Functions on Noncommutative Tori

Ordinary theta functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta functions as holomorphic elements of projective modules over noncommutative tori (theta vectors). The theory of these new objects is not only more general, but also much simpler than the theory of ordinary theta-functions. It seems that the theory of theta vectors should be closely related to Manin's theory of quantized theta functions, but we don't analyze this relation.     

New concept of relativistic invariance in noncommutative space-time: twisted poincare symmetry and its implications

We present a systematic framework for noncommutative (NC) quantum field theory (QFT) within the new concept of relativistic invariance based on the notion of twisted Poincare symmetry, as proposed by Chaichian et al. [Phys. Lett. B 604, 98 (2004)]. This allows us to formulate and investigate all fundamental issues of relativistic QFT and offers a firm frame for the classification of particles according to the representation theory of the twisted Poincare symmetry and as a result for the NC versions of CPT and spin-statistics theorems, among others, discussed earlier in the literature. As a further application of this new concept of relativism we prove the NC analog of Haag's theorem.     

非对易OrbifoldR4/G上的量子态及孤子解

求得二维由广义坐标和广义动量构成的一般二次型哈密顿量的基态,由此可以求得各能级的本征态.由于四维非对易空间在转动群GSO(4)下的坐标的不变二次型可以正则化为这类哈密顿量,因此得到了非对易空间R4上转动不变的态矢量.当G是SO(4)的有限子群时候它们是R4/G这种非对易Orbifold上的态矢量.由此可以得到其上的孤子解.     

Theta functions,modular invariance,and strings

We use Quillen's theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure dependence of the chiral Dirac determinant on a Riemann surface is given by Riemann's theta function. We use this result to investigate the modular invariance of multiloop heterotic string amplitudes.     

Instantons on General Noncommutative R4

We study the U(1) and U(2) instanton solutions of gauge theory on general noncommutative R4. In allcases considered we obtain explicit results for the projection operators. In some cases we computed numerically theinstanton charge and found that it is an integer independent of the noncommutative parameters θ1,2.     

A noncommutative deformation of topological field theory

Cohomological Yang–Mills theory is formulated on a noncommutative differentiable four manifold through the -deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the -deformation of Donaldson invariants and they are interpreted as a mapping between the Chevalley–Eilenberg homology of noncommutative spacetime and the Chevalley–Eilenberg cohomology of noncommutative moduli of instantons. In the process we find that in the weak coupling limit the quantum theory is localized at the moduli space of noncommutative instantons.