Vector meson masses in two-dimensional SU(N_C)lattice gauge theory with massive quarks

Using an improved lattice Hamiltonian with massive Wilson quarks a variational method is applied to study the dependence of the vector meson mass Mv on the quark mass m and the Wilson parameter r in two-dimensional SU（Nc） lattice gauge theory. The numerical results show that for Nc = 2, 3, 4, 5, 6, 7, ..., in the scaling window 1 ≤ 1/g^2 ≤ 2, Mv/g is approximately linear in m, but Mv/g obviously does not depend on r （this differs from the quark condensate）. Particularly for m → 0 our numerical results agree very well with Bhattacharya＇s analytical strong coupling result in the continuum, and the value of （δMv/δm） ｜m=0 in two-dimensional SU（Nc） lattice gauge theory is very close to that in Schwinger model.

LEPTON MIXING-RIGHT SYMMETRY ELECTROWEAK GAUGE THEORY AND v_3 NEUTRINO DECAY

In this paper, we introduce four models for the discrete horizontal symmetry in the gauge theory of electroweak interactions with left-right symmetry （i. e., the SU（2）L × SU（2）R × U（1） model） to obtain four sets of the mixing angles among the different generations of leptons separately. In light of the corresponding mass relations obtained and the preliminary result for mv1 and mv2, we estimate the possible value of mv3 and discuss the various physical effects arising from the lepton mixing and non-vanishing mass of neutrinos in these four models, such as their influences on the determination of quark mixing angle and the representation of the μ-e universality, the neutrino oscillations and their applications in astrophysics and so on, with special emphasis on the life-time and various possible decay modes of v3 （its mass is about 2×102 Mev in Model B） so as to give a clue to experimental detection of v3.

ELECTRICALLY CHARGED SOLITONS IN GAUGE FIELD THEORY

Monopoles and vortices are well known magnetically charged soliton solutions of gauge field equations. Extending the idea of Dirac on monopoles, Schwinger pioneered the concept of solitons carrying both electric and magnetic charges, called dyons, which are useful in modeling elementary particles. Mathematically, the existence of dyons presents interesting variational partial differential equation problems, subject to topological constraints. This article is a survey on recent progress in the study of dyons.

Inverse scattering method and soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields

A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.

Ashtekar-Kodama Gravity as a Classical and Quantum Extension of Loop Quantum Gravity

This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and in the quantum regime a full renormalizable quantum gauge field theory. The three fundamental constraints (hamiltonian, gaussian and diffeomorphism) were formulated in 3-dimensional spatial form within LQG in Ashtekar formulation using the notion of the Kodama state with positive cosmological constant Λ. We introduce a 4-dimensional covariant version of the 3-dimensional (spatial) hamiltonian, gaussian and diffeomorphism constraints of LQG. We obtain 32 partial differential equations for the 16 variables Emn (E-tensor, inverse densitized tetrad of the metric) and 16 variables Amn (A-tensor, gravitational wave tensor). We impose the boundary condition: for large distance the E-generated metric g(E) becomes the GR-metric g (normally Schwarzschild-spacetime). The theory based on these Ashtekar-Kodama (AK) equations, and called in the following Ashtekar-Kodama (AK-) gravity has the following properties. • For Λ = 0 the AK equations become Einstein equations, A-tensor is trivial (constant), and the E-generated metric g(E) is identical with the GR-metric g. • When the AK-equations are developed into a Λ-power series, the Λ-term yields a gravitational wave equation, which has only at least quadrupole wave solutions and becomes in the limit of large distance r the (normal electromagnetic) wave equation. • AK-gravity, as opposed to GR, has no singularity at the horizon: the singularity in the metric becomes a (very high) peak. • AK-gravity has a limit scale of the gravitational quantum region 39 μm, which emerges as the limit scale in the objective wave collapse theory of Gherardi-Rimini-Weber. In the quantum region, the AK-gravity becomes a quantum gauge theory (AK quantum gravity) with the Lie group extended SU(2) = ε-tensor-group(four generators) as gauge group and a corresponding covariant derivative. • AK quantum gravity is fully renormalizable, we derive its Lagrangian, which is dimensionally renormalizable, the normalized one-graviton wave function, the graviton propagator, and demonstrate the calculation of cross-section from Feynman diagrams.

Gauge Formulation of Heaviside’s Equations

A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside’s “linearized” equations are known as the “weak field approximation”. When derived from the primordial field equation, there is no mention of field strength;the assumption that the primordial field was predominant at the big bang rather suggests that ultra-strong fields are governed by the equations. This aspect has physical significance, so we explore the assumption by formulating the gauge field version of Heaviside’s theory. We compare with recent linearized gravity formulations and discuss the significance of differences.

Quantum simulation of lattice gauge theories on superconducting circuits:Quantum phase transition and quench dynamics

Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.

Effects of Compactification on Free Massive Scalar Fields in Five-Dimensional Space-Time with an Extra Time Dimension: Analysing Some Results

This paper deals with some aspects of two-time physics (i.e., 2T + 3S five-dimensional space) for a Minkowski-like space with distinct speeds of causality for the time dimensions. Detailed calculations are provided to obtain results of Kaluza-Klein type compactification for free massive scalar fields and abelian free gauge fields. As already indicated in the literature, a tower of massive fields results from the compactification with mass terms having signs opposite to those of the ones appearing in other five-dimensional theories with an extra space dimension. We perform elaborate numerical calculations to highlight the magnitude of the imaginary masses and ask if we need to explore alternative compactification techniques.

Is Yang-Mills theory unitary in fractional spacetime dimensions?

We present concrete evidence that Yang-Mills theory exhibits non-unitarity in non-integer spacetime dimensions.This violation of unitarity stems from evanescent operators that,while vanishing in four dimensions,are non-zero in general d dimensions.We demonstrate that these evanescent operators lead to the emergence of both negative-norm states and complex anomalous dimensions.

The Primordial Principle of Self-Interaction

The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed to produce this convergence. Our theory proposes one primordial field and analyzes the evolution of this field. The key assumption is that only the primordial field exists—if any change is to occur, it must be based upon self-interaction, as there is nothing other than the field itself to interact with. This can be formalized as the Principle of Self-interaction and the consequences explored. I show that this leads to the linearized Einstein field equations and discuss the key ontological implications of the theory.

Solving local constraint condition problem in slave particle theory with the BRST quantization

With the Becchi-Rouet-Stora-Tyutin(BRST) quantization of gauge theory,we solve the long-standing difficult problem of the local constraint conditions,i.e.the single occupation of a slave particle per site,in the slave particle theory.This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier λ_(i) which ensures the constraint:in the Hamiltonian formalism of the theory,λ_(i) is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism,λ_(i)(t) becomes time-dependent and plays a role of gauge field.This implies that the redundant degrees of freedom of λ_(i)(t) are introduced and must be removed by the additional constraint,the gauge fixing condition(GFC) ?_tλ_(i)(t)= 0.In literature,this GFC was missed.We add this GFC and use the BRST quantization of gauge theory for Dirac's first-class constraints in the slave particle theory.This GFC endows λ_(i)(t) with dynamics and leads to important physical results.As an example,we study the Hubbard model at half-filling and find that the spinon is gapped in the weak U and the system is indeed a conventional metal,which resolves the paradox that the weak coupling state is a superconductor in the previous slave boson mean field(MF) theory.For the t-J model,we find that the dynamic effect of λ_(i)(t) substantially suppresses the d-wave pairing gap and then the superconducting critical temperature may be lowered at least a factor of one-fifth of the MF value which is of the order of 1000 K.The renormalized T_c is then close to that in cuprates.

The Nature of Inertial and Vacuum Gravitational Field

The uniformly accelerated motion is studied in the framework of gauge theory of gravity. It is found that, when an inertial reference system is transformed into a uniformly accelerated system by a local gravitational gauge transformation, a non-trivial gravitational gauge field appears. If there is a mass point in the new reference frame, there will be a non-trivial gravitational force acting on it. The nature and the characteristic of this new force are completely the same as those of the traditional inertial force. This new gravitational force is considered to be the inertial force. Therefore, the nature of inertial force is gravity, which is the basic idea of the equi-valence principle.

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP（1,5） and the global Poincar′e symmetry P（1,5）= SO（1,5） P^1,5 as well as the charge spin gauge symmetry SU（2）. The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.

Holographic operator product expansion of loop operators in the N=4~SO(N) super Yang-Mills theory

In this study,we compute the correlation functions of Wilson(-'t Hooft)loops with chiral primary operators in the N=4 supersymmetric Yang-Mills theory with SO(N)gauge symmetry,which has a holographic dual description of the Type IIB superstring theory on the AdS_(5)×Rp^(5)background.Specifically,we compute the coefficients of the chiral primary operators in the operator product expansion of Wilson loops in the fundamental representation,Wilson-'t Hooft loops in the symmetric representation,Wilson loops in the anti-fundamental representation,and Wilson loops in the spinor representation.We also compare these results to those of the N=4 SU(N)super Yang-Mills theory.

Covariant open string field theory on multiple Dp-branes

We study covariant open bosonic string field theories on multiple Dp-branes by using the deformed cubic string field theory, which is equivalent to string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple Dp-branes, we obtain the field theoretical effective action in the zero-slope limit. On multiple D0-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind （BFSS） matrix model. We also discuss the relation between open string field theory on multiple D-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya （IKKT） matrix model. The covariant open string field theory on multiple Dp-branes could be useful to study the non-perturbative properties of quantum field theories in （p＋1）-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using covariant string field theory.

Deformed integrable models from holomorphic Chern-Simons theory

We study the approaches to two-dimensional integrable field theories via a six-dimensional(6 D) holomorphic Chern-Simons theory defined on twistor space. Under symmetry reduction, it reduces to a 4 D Chern-Simons theory, while under solving along fibres it leads to a four-dimensional(4 D) integrable theory, the anti-self-dual Yang-Mills or its generalizations. From both 4 D theories, various two-dimensional integrable field theories can be obtained. In this work, we try to investigate several twodimensional integrable deformations in this framework. We find that the λ-deformation, the rational η-deformation, and the generalized λ-deformation can not be realized from the 4 D integrable model approach, even though they could be obtained from the 4 D Chern-Simons theory. The obstacle stems from the incompatibility between the symmetry reduction and the boundary conditions. Nevertheless, we show that a coupled theory of the λ-deformation and the η-deformation in the trigonometric description could be obtained from the 6 D theory in both ways, by considering the case that(3, 0)-form in the 6 D theory is allowed to have zeros.

A new gravitational model for dark energy

A new gravitational model for dark energy is presented based on the model of de Sitter gauge theory of gravity. In the model, in addition to the cosmological constant, the homogeneous and isotropic torsion and its coupling with curvature play an important role for dark energy. The model may supply the universe with a natural transit from decelerating expansion to accelerating expansion.

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.

Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes revisited

We provide a new proof of Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes.As a key step,we explicitly demonstrate the cancellation of spurious poles originating from the maximally helicity violating vertices in these rules.To achieve this,we introduce specially-defined two-off-shell-line sub-amplitudes and examine their residues at spurious poles.