Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing

The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.

Vector and Spinor Decomposition of SU（2） Gauge Potential, Their Equivalence, and Knot Structure in SU（2） Chern-Simons Theory

In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.

Inner Structure of Statistical Gauge Potential in Chern-Simons-Ginzburg-Landau Theory

Based on the decomposition theory of the U（1） gauge potential, the inner structure of the statistical gauge potential in the Chern-Simons-Ginzburg-Landau （CSGL） theory is studied. We give a new creation mechanism of the statistical gauge potential, Furthermore, making use of the b-mapping topological current theory, we obtain the precise topological expression of the statistical magnetic field, which takes the topological information of the vortices.

R^(1+1)中Maxwell-Chern-Simons-Higgs模型解的L^(∞)估计

用能量守恒估计和特征线估计的方法解决(1+1)维Maxwell-Chern-Simons-Higgs模型解的Sobolev范数增长性估计问题,给出模型有限能量解的一阶导数的L^(∞)估计,并通过改进指数增长得到解的H^(2)范数的多项式增长.

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.

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.

Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge Theory

In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.

A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model

The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently.The standard model is defined perturbatively and describes all elementary particles(except gravitons)very well.However,for a long time,we do not know if we can have a non-perturbative definition of the standard model as a Hamiltonian quantum mechanical theory.Here we propose a way to give a modified standard model(with 48 two-component Weyl fermions)a non-perturbative definition by embedding the modified standard model into an SO(10)chiral gauge theory.We show that the SO(10)chiral gauge theory can be put on a lattice(a 3D spatial lattice with a continuous time)if we allow fermions to interact.Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volume.More generally,using the defining connection between gauge anomalies and the symmetry-protected topological orders,one can show that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension.

Comparative study on atomic ionization in bicircular laser fields by length and velocity gauges S-matrix theory

Ionization of atoms in counter-rotating and co-rotating bicircular laser fields is studied using the S-matrix theory in both length and velocity gauges.We show that for both the bicircular fields,ionization rates are enhanced when the two circularly polarized lights have comparable intensities.In addition,the curves of ionization rate versus the field amplitude ratio of the two colors for counter-rotating and co-rotating fields coincide with each other in the length gauge case at the total laser intensity 5×10^14 W/cm^2,which agrees with the experimental observation.Moreover,the degree of the coincidence between the ionization rate curves of the two bicircular fields decreases with the increasing field amplitude ratio and decreasing total laser intensity.With the help of the ADK theory,the above characteristics of the ionization rate curves can be well interpreted,which is related to the transition from the tunneling to multiphoton ionization mechanism.

Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algebra g(T2). In this paper, we construct the linearly realized gauge theory of the SDIFF(T2)loc1al-generalized Kac-Moody G(T2) symmetry.

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.

Independent Plaquette Trial Action for 4-Dimensional Lattice Gauge Theory

Based on the explicit expressions of the plaquette formulations, the independent plaquette trial action for 4-dimensional lattice gauge theory is introduced. As an example, the mean plaquette energy EP for the SU(2) lattice gauge theory is calculated by using action variational approach with the independent trial action. The results are in good agreement with the Monte Carlo results in the strong coupling and the crossover region, and the curve is smooth in the whole region, which show that 4-dimensional SU(2) theory has only a single, confining phase. The unwanted discontinuity of EP given by the single link trial action, which is used in the earlier variational calculations has been avoided.

Faddeev-Jackiw Quantization of the Gauge Invariant Version of the Linear Self-Dual constrained Theory

The Faddeev-Jackiw quantization procedure is applied to the gauge invariant version of the linear self-dual constrained theory.The equivalence of the gauge invariant and the gauge noninvariant versions is discussed.

THE EXACT GROUND STATE OF A HAMILTONIAN LATTICE GAUGE THEORY

A modified hamiltonian of lattice gauge theory including 2-plaquette,interaction has been studied.We have found the exact ground state of the theory.

ANALYTICAL METHOD IN LATTICE GAUGE THEORY AT FINITE TEMPERATURE

A variational-cumulant expansion method at finite temperature is developed in the lattice gauge theory.The order parameter<L>(the statistical average of the thermal loop)is analytically calculated to the 3rd order cumulant expansion.The change of<L>=0 to<L>≠0 clearly shows the existence of a deconfine phase transition of 2nd order in agreement with the latest Monte Carlo simulations.

Schwarzschild-de-Sitter Solution in Quantum Gauge Theory of Gravity

We use the theory based on the gravitational gauge group G to obtain a spherical symmetric solution of the field equations for the gravitational potentials on a Minkowski space-time. The gauge group G is defined and then we introduce the gauge-covariant derivative Dμ. The strength tensor of the gravitational gauge field is also obtained and a gauge-invariant Lagrangian including the cosmological constant is constructed. A model whose gravitational gauge potentials A^α μ （x） have spherical symmetry, depending only on the radial coordinate τ is considered and an analytical solution of these equations, which induces the Schwarzschild-de-Sitter metric on the gauge group space, is then determined. All the calculations have been performed by GR Tensor II computer algebra package, running on the Maple V platform, along with several routines that we have written for our model.

THE PHASE STRUCTURE FOR TWO PARAMETER ACTIONS IN SU(2)LATTICE GAUGE THEORY

The variational method has been applied to investigating the phase diagrams of the two parameter actions containing TrU(P)^(3) term in SU(2)lattice gauge theory.The result is in agreement with that obtained by Monte Carlo simulations.This can be helpful to understand the mechanism of the phase transitions.

The Fate of Supersymmetry in Quantum Field Theories

We analyze the significance of supersymmetry in two topological models and the standard model (SM). We conclude that the two topological field theory models favor hidden supersymmetry. The SM superpartners, instead, have not been found.

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.

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.