An Interacting Gauge Field Theoretic Model for Hodge Theory: Basic Canonical Brackets

We derive the basic canonical brackets amongst the creation and annihilation operators for a two （1 ＋ 1）- dimensional （2D） gauge field theoretic model of an interacting Hodge theory where a U（1） gauge field （Aμ） is coupled with the fermionic Dirac fields （ψ and ψ）. In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries （and the concept of their generators） that are present in the theory. We do not use the definition of the canonical conjugate momenta （corresponding to the basic fields of the theory） anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries （and corresponding generators） provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.     

New Terms for Compact Form of Electroweak Chiral Lagrangian

The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.     

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.     

Diverse solid and supersolid phases of bosons in a triangular lattice

We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.     

A Linearization Approach for Rational Nonlinear Models in Mathematical Physics

In this paper,a novel method for linearization of rational second order nonlinear models is discussed.In particular,we discuss an application of the δ expansion method(created to deal with problems in Quantum Field Theory) which will enable both the linearization and perturbation expansion of such equations.Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations.Higher order perturbation theories can then be obtained in terms of such special functions.One benefit to such a method is that it may be applied even to models without small physical parameters,as the perturbation is given in terms of the degree of nonlinearity,rather than any physical parameter.As an application,we discuss a method of linearizing the six Painleve equations by an application of the method.In addition to highlighting the benefits of the method,we discuss certain shortcomings of the method.     

Seiberg-Witten/Whitham Equations and Instanton Corrections in Ν = 2 Supersymmetric Yang-Mills Theory

We obtain the instanton correction recursion relations for the low energy effective prepotential in pure Ν = 2SU(n) supersymmetric Yang-Mills gauge theory from Whitham hierarchy and Seiberg-Witten/Whitham equations. These formulae provide us a powerful tool to calculate arbitrary order instanton corrections coefficients from the perturbative contributions of the effective prepotential in Seiberg-Witten gauge theory. We apply this idea to evaluate one-and two-order instanton corrections coefficients explicitly in SU(n) case in detail through the dynamical scale parameter expressed in terms of Riemann's theta-function.     

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     

Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein-Gordon equation and Dirac equation. We investigate the scalar field and φ4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space.     

New Electroweak Model Without a Higgs Particle

A new unified electroweak model is proposed in this paper,In this unified electroweak model,Higgs echanism is not used.So no Higgs particle exists in the model.In order to keep the masses of intermediate gauge bosons non-zero,two sets of gauge fields will be introduced.In order to introduce symmetry breaking and to help to introduce the masses of all fileds.a vacuum potential is needed.Except for those terms concerning Higgs particle,the fundamental dynamical properties of this model are similar to those of the standard model.And in a proper limit,this model with approximately return to the standard model.The purpose of this paper is not to say that the Higgs particle does not exist in Nature,it is only to prove that,without a Higgs particle,we can also set up a unified electroweak model which is consistent with present experiments.     

Local Poincaré Symmetry in Gauge Theory of Gravity

It is well known that the Poincaré gauge theories of gravity do not have the structure of a standard gauge theory. Nevertheless, we show that a general form of action for the gravitational gauge fields in the gauge theory does possess local Poincaré invariance.     

A gauge theory for two-band model of Chern insulators and induced topological defects

In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from which arise two types of topological defects,monopoles and e2 merons.We focus on the topological number in the Hall conductance σ_xy=e²/hC,where C is the Chern number.It is discovered that in the monopole case C is indeterminate,while in the meron case C takes different values,due to a varying on-site energy m.As a typical example,we apply this method to the square lattice and compute the winding numbers(topological charges)of the defects;the C-evaluations we obtain reproduce the results of the usual literature.Furthermore,based on the gauge theory we propose a new model to obtain the high Chern numbers|C|=2,4.     

Hyperelliptic Function Solutions of Three Genus for KP Equation Using Direct Method

In this paper, we will use a simple and direct method to obtain some particular solutions of （2＋1）- dimensional and （3＋ 1）-dimensional KP equation expressed in terms of the Kleinian hyperelliptic functions for a given curve y^2 = f（x） whose genus is three. We observe that this method generalizes the auxiliary method, and can obtain the hyperelliptic functions solutions.     

Theory for quarkonium:from NRQCD factorization to soft gluon factorization

We demonstrate that the recently proposed soft gluon factorization(SGF)is equivalent to the nonrelativistic QCD(NRQCD)factorization for heavy quarkonium production or decay,which means that,for any given process,these two factorization theories are either both valid or both violated.We use two methods to arrive at this conclusion.In the first method,we apply the two factorization theories to the physical process J/ψ→e^+e^-.Our explicit calculation shows that both SGF and NRQCD can correctly reproduce the low energy physics of full QCD,and the two factorizations are thus equivalent.In the second method,by using equations of motion,we successfully deduce SGF from NRQCD effective field theory.By identifying SGF with NRQCD factorization,we establish relations between the two factorization theories and prove the generalized Gremm-Kapustin relation as a byproduct.Compared with the NRQCD factorization,the advantage of SGF is that it resums the series of relativistic corrections originating from kinematic effects to all powers,yielding better convergence of the relativistic expansion.     

From geometry to non-geometry via T-duality

Reconsideration of the T-duality of the open string allows us to introduce some geometric features in non-geometric theories.First,we have found what symmetry is T-dual to the local gauge transformations.It includes transformations of background fields but does not include transformations of the coordinates.According to this we have introduced a new,up to now missing term,with additional gauge field A_i~D(D denotes components with Dirichlet boundary conditions).It compensates non-fulfilment of the invariance under such transformations on the end-points of an open string,and the standard gauge field A_a~N(N denotes components with Neumann boundary conditions)compensates non-fulfilment of the gauge invariance.Using a generalized procedure we will perform T-duality of vector fields linear in coordinates.We show that gauge fields A_a~Nand A_i~Dare T-dual to A_D~aand A_N~irespectively.We introduce the field strength of T-dual non-geometric theories as derivatives of T-dual gauge fields along both T-dual variable y_μand its double?y_μ.This definition allows us to obtain gauge transformation of non-geometric theories which leaves the T-dual field strength invariant.Therefore,we introduce some new features of non-geometric theories where field strength has both antisymmetric and symmetric parts.This allows us to define new kinds of truly non-geometric theories.     

Spin-Spin Interactions in Gauge Theory of Gravity, Violation of Weak Equivalence Principle and New Classical Test of General Relativity

For a long time, it has been generally believed that spin-spin interactions can only exist in a theory where Lorentz symmetry is gauged, and a theory with spin-spin interactions is not perturbatively renormalizable. But this is not true. By studying the motion of a spinning particle in gravitational field, it is found that there exist spin-spin interactions in gauge theory of gravity. Its mechanism is that a spinning particle will generate gravitomagnetic field in space-time, and this gravitomagnetic field will interact with the spin of another particle, which will cause spin-spin interactions. So, spin-spin interactions are transmitted by gravitational field. The form of spin-spin interactions in post Newtonian approximations is deduced. This result can also be deduced from the Papapetrou equation. This kind of interaction will not affect the renormalizability of the theory. The spin-spin interactions will violate the weak equivalence principle, and the violation effects are detectable. An experiment is proposed to detect the effects of the violation of the weak equivalence principle.     

Complete synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller

In this paper, we apply a simple adaptive feedback control scheme to synchronize two bi-directionally coupled chaotic systems. Based on the invariance principle of differential equations, sufficient conditions for the global asymptotic synchronization between two bi-directionally coupled chaotic systems via an adaptive feedback controller are given. Unlike other control schemes for bi-directionally coupled systems, this scheme is very simple to implement in practice and need not consider coupling terms. As examples, the autonomous hyperchaotic Chen systems and the new non-autonomous 4D systems are illustrated. Numerical simulations show that the proposed method is effective and robust against the effect of weak noise.     

Nernst Theorem and Statistical Entropy of 5-Dimensional Rotating Black Hole

In this paper, by using quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of the 5-dimensional rotating black hole. Then via the improved brick-wall method and membrane model, we calculate the entropy of Bose field and Fermi field of the black hole. And it is obtained that the entropy of the black hole is not only related to the area of the outer horizon but also is the function of inner horizon‘s area. In our results, there are not the left out term and the divergent logarithmic term in the original brick-wall method.The doubt that why the entropy of the scalar or Dirac field outside the event horizon is the entropy of the black hole in the original brick-wall method does not exist. The influence of spinning degeneracy of particles on entropy of the black hole is also given. It is shown that the entropy determined by the areas of the inner and outer horizons will approach zero,when the radiation temperature of the black hole approaches absolute zero. It satisfies Nernst theorem. The entropy can be taken as the Planck absolute entropy. We provide a way to study higher dimensional black hole.     

Nernst Theorem and Statistical Entropy of 5-Dimensional Rotating Black Hole

In this paper, by using quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of the 5-dimensional rotating black hole. Then via the improved brick-wall method and membrane model, we calculate the entropy of Bose field and Fermi field of the black hole. And it is obtained that the entropy of the black hole is not only related to the area of the outer horizon but also is the function of inner horizon‘s area. In our results, there are not the left out term and the divergent logarithmic term in the original brick-wall method.The doubt that why the entropy of the scalar or Dirac field outside the event horizon is the entropy of the black hole in the original brick-wall method does not exist. The influence of spinning degeneracy of particles on entropy of the black hole is also given. It is shown that the entropy determined by the areas of the inner and outer horizons will approach zero,when the radiation temperature of the black hole approaches absolute zero. It satisfies Nernst theorem. The entropy can be taken as the Planck absolute entropy. We provide a way to study higher dimensional black hole.     

Constraining qqtt operators from four-top production:a case for enhanced EFT sensitivity

Recently, experimental collaborations have reported 0(10) upper limits on the signal strength of fourtop production at the LHC. Surprisingly, we find that the constraining power of four-top production on the qqtt type of operators is already competitive with the measurements of top-pair production, even though the precision level of the latter is more than two orders of magnitude better. This is explained by the enhanced sensitivity of the four-top cross section to qqtt operators, due to multiple insertion of operators in the squared amplitude, and to the large threshold energy of four-top production. We point out that even though the dominant contribution beyond the standard model comes from the O(C~4/Λ~8) terms, the effective field theory expansion remains valid for a wide range of underlying theories. Considering the possible improvements of this measurement with higher integrated luminosity, we believe that this process will become even more crucial for probing and testing the standard model deviations in the top-quark sector, and will eventually provide valuable information about the top-quark properties,leading to significant improvements in precision top physics.     

Solitary Solution of Discrete mKdV Equation by Homotopy Analysis Method

In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows that homotopy analysis method is effective and validity in solving hybrid nonlinear problems, including solitary solution of difference-differential equation.