An Outline of the Grand Unified Theory of Gauge Fields

This paper attempts to propose a grand unified guiding principle of gauge fields from the mathematical and physical picture of fiber bundles: it is believed that our universe may have more fundamental interactions than the four fundamental interactions, and the gauge fields of these fundamental interactions are just a unified gauge potential on the fiber bundle manifold or the components connected to the bottom manifold, that is, our universe;these components can meet the transformation of gauge potential, and even can be transformed from a fundamental interaction gauge potential to another fundamental interaction gauge potential, and can be summarized into a unified equation, namely the expression of the generalized gauge equation, corresponding to the gauge transformation invariance;so gauge transformation invariance is a necessary condition to unify field theory, but quantization of field is not a necessary condition;the four (or more) fundamental interaction fields of the universe are unified into a universal gauge field defined by the connection of the principal fiber bundle on the cosmic base manifold.

New Mechanism for Mass Generation of Gauge Field

A new mechanism for mass generation of gauge field is discussed in this paper. By introducing two sets of gauge fields and making the variations of these two sets of gauge fields compensated each other under local gauge transformations, the mass term of gauge fields is introduced into the Lagrangian without violating the local gauge symmetry of the Lagrangian. This model is a renormalizable quantum model.

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.

Supersymmetric U(1) Gauge Field Theory with Massive Gauge Field

A new mechanism to introduce the mass of gauge field in supersymmetric gauge theory is discussed. The model has the strict local gauge symmetry and supersymmetry. Because we introduce two vector superfields simultaneously, the model contains a massive gauge field as well as a massless gauge field.

Quench dynamics of ultracold atoms in one-dimensional optical lattices with artificial gauge fields

We study the quench dynamics of noninteracting ultracold atoms loaded in one-dimensional （1D） optical lattices with artificial gauge fields, which are modeled by lattices with complex hopping coefficients. After suddenly changing the hopping coefficient, time evolutions of the density distribution, momentum distribution, and mass current at the center are studied for both finite uniform systems and trapped systems. Effects of filling factor, system size, statistics, harmonic trap, and phase difference in hopping are identified, and some interesting phenomena show up. For example, for a finite uniform fermionic system shock and rarefaction wave plateaus are formed at two ends, whose wave fronts move linearly with speed equaling to the maximal absolute group velocity. While for a finite uniform bosonic system the whole density distribution moves linearly at the group velocity. Only in a finite uniform fermionic system there can be a constant quasi- steady-state current, whose amplitude is decided by the phase difference and filling factor. The quench dynamics can be tested in ultracold atoms with minimal modifications of available experimental techniques, and it is a very interesting and fundamental example of the transport phenomena and the nonequilibrium dynamics.

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.

Topological Lifshitz transition and novel edge states induced by non-Abelian SU(2)gauge field on bilayer honeycomb lattice

We investigate the SU(2)gauge effects on bilayer honeycomb lattice thoroughly.We discover a topological Lifshitz transition induced by the non-Abelian gauge potential.Topological Lifshitz transitions are determined by topologies of Fermi surfaces in the momentum space.Fermi surface consists of N=8 Dirac points atπ-flux point instead of N=4 in the trivial Abelian regimes.A local winding number is defined to classify the universality class of the gapless excitations.We also obtain the phase diagram of gauge fluxes by solving the secular equation.Furthermore,the novel edge states of biased bilayer nanoribbon with gauge fluxes are also investigated.

Theoretical Maxwell's Equations, Gauge Field and Their Universality Based on One Conservation Law

The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codiffcrential forms are pointed out： they represent the tangent surface and the normal surface fluxes of a tensor, reslpetivcly. The definitions of the divergence and the curl of a 2D surface flux of a tensor arc obtained. Maxwell＇s equations, namely, the constraction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law （ mass or fluid flux quantity and so on） and the feature of central field （or its composition）. By the feature of central field （or its composition）, the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory （ a magnetic monopole has no effect on electric current just like a couple hasing no effect on the sum of forces） axe presented： magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell＇s equations.

The synthetic gauge field and exotic vortex phase with spin-orbital-angular-momentum coupling

Ultracold atoms endowed with tunable spin-orbital-angular-momentum coupling(SOAMC)represent a promising avenue for delving into exotic quantum phenomena. Building on recent experimental advancements, we propose the generation of synthetic gauge fields, and by including exotic vortex phases within spinor Bose-Einstein condensates, employing a combination of a running wave and Laguerre-Gaussian laser fields. We investigate the ground-state characteristics of the SOAMC condensate, revealing the emergence of exotic vortex states with controllable orbital angular momenta. It is shown that the interplay of the SOAMC and conventional spin-linear-momentum coupling induced by the running wave beam leads to the formation of a vortex state exhibiting a phase stripe hosting single multiply quantized singularity. The phase of the ground state will undergo the phase transition corresponding to the breaking of rotational symmetry while preserving the mirror symmetry. Importantly, the observed density distribution of the ground-state wavefunction, exhibiting broken rotational symmetry, can be well characterized by the synthetic magnetic field generated through light interaction with the dressed spin state. Our findings pave the way for further exploration into the rotational properties of stable exotic vortices with higher orbital angular momenta against splitting in the presence of synthetic gauge fields in ultracold quantum gases.

Cyclotron dynamics of a Bose—Einstein condensate in a quadruple-well potential with synthetic gauge fields

We investigate the cyclotron dynamics of Bose-Einstein condensate(BEC)in a quadruple-well potential with synthetic gauge fields.We use laser-assisted tunneling to generate large tunable effective magnetic fields for BEC.The mean position of BEC follows an orbit that simulated the cyclotron orbits of charged particles in a magnetic field.In the absence of atomic interaction,atom dynamics may exhibit periodic or quasi-periodic cyclotron orbits.In the presence of atomic interaction,the system may exhibit self-trapping,which depends on synthetic gauge fields and atomic interaction strength.In particular,the competition between synthetic gauge fields and atomic interaction leads to the generation of several discontinuous parameter windows for the transition to self-trapping,which is obviously different from that without synthetic gauge fields.

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.

Gravitational Gauge Interactions of Dirac Field

Gravitational interactions of Dirac field are studied in this paper. Based on gauge principle, quantum gauge theory of gravity, which is perturbatively renormalizable, is formulated in the Minkowski space-time. In quantum gauge theory of gravity, gravity is treated as a kind of fundamental interactions, which is transmitted by gravitational gauge field, and Dirac field couples to gravitational field through gravitational gauge covariant derivative. Based on this theory, we can easily explain gravitational phase effect, which has already been detected by COW experiment.

Optical quantum simulation of Abelian gauge field using cold atomic ensembles coupled with arrays of optical cavities

A potentially practical scheme is proposed to realize optical quantum simulation of artificial Abelian gauge field in a scalable architecture consisting of cold atomic ensembles with optical cavities.In the present model,the collective excitations of cold atomic ensembles can be converted to the bosonic modes within the low-excitation limit,where the structure of two-dimension(2D)square plaquette enables the polaritons to move like a charged particle subjected to an external magnetic field.We find that the energy spectrum of this hybrid system exhibits a shape of Hofstadter buttery.Our work provides a different perspective to the quantum simulation of condensed matter and many-body physics in the context of cavity quantum electrodynamics.The experimental feasibility are justified using the existing techniques.

Gauge Gravitational Field in a Fractal Space-Time

Considering the fractal structure of space-time, the scale relativity theory in the topological dimension DT = 2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner- Nordstrom type metric 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.

Gravitational Shielding Effect in Gauge Theory of Gravity

In 1992,E.E.Podkletnov and R.Nieminen found that under certain conditions,ceramic superconductor with composite structure reveals weak shielding properties against gravitational force.In classical Newton's theory of gravity and even in Einstein's general theory of gravity,there are no grounds of gravitational shielding effects.But in quantum gauge theory of gravity,the gravitational shielding effects can be explained in a simple and natural way.In quantum gauge theory of gravity,gravitational gauge interactions of complex scalar field can be formulated based on gauge principle.After spontaneous symmetry breaking,if the vacuum of the complex scalar field is not stable and uniform,there will be a mass term of gravitational gauge field.When gravitational gauge field propagates in this unstable vacuum of the complex scalar field,it will decays exponentially,which is the nature of gravitational shielding effects.The mechanism of gravitational shielding effects is studied in this paper,and some main properties of gravitational shielding effects are discussed.

Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.

Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schroedinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schroedinger equation, which can explain the gravitational phase effects found in COW experiments. And because of this Newtonian gravitational potential, a quantum particle in the earth＇s gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.

Linear Transformation Theory of Quantum Field Operators and Its Applications

We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.