Landau-Lifschitz铁磁方程的Hamilton理论和规范变换

对完全各向同性Heisenberg铁磁链的LandauLifschitz方程的Hamilton理论建立中，Hamilton量的坐标积分和谱参数积分两种表示式不能协调地从单一守恒量导出的问题，利用规范变换完善地解决了.并可推广后处理非各向同性铁磁链的LandauLifschitz方程的Hamilton理论. 关键词： 规范变换 LandauLifschitz方程 守恒量 Hamilton理论     

Kosterlitz-Thouless transition for the finite-temperatured=2+1,U(1) Hamiltonian lattice gauge theory

We prove that in thed=2+1,U(1) Hamiltonian (continuous time) lattice gauge theory the confining potential between two static external charges grows logarithmically with their distance, at sufficiently high temperatures. As it is known that for zero or low temperatures and large coupling constant the model confines linearly, we have therefore established the existence of a Kosterlitz-Thouless transition. Our results are based on a Mermin-Wagner type of argument combined with correlation inequalities and known results for the two-dimensional (spin) Villain model.     

Poincaré gauge theory with coupled even and odd parity spin‐0 modes: Cosmological normal modes

We are investigating the dynamics of a new Poincaré gauge theory of gravity model, which has cross coupling between the spin‐0⁺ and spin‐0^‐ modes. To this end we are considering a very appropriate situation – homogeneous‐isotropic cosmologies – which is relatively simple, and yet all the modes have non‐trivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies. Here the first order equations obtained from an effective Lagrangian are linearized and the normal modes are found. These turn out to control the asymptotic late time cosmological normal modes. Numerical evolution confirms the late time asymptotic approximation and shows the expected effects of the cross parity pseudoscalar coupling.     

Applications of the Poincaré sphere in polarization metrology

The Poincaré sphere representation of polarization states is used to derive two auxiliary equations for phase retardance measurements. These equations, in addition to another two previously derived equations, allow for extending the range of validity of a model for calibrating phase plates in pairs. In another application, the sphere is used to explain a new method for identifying the principal axes of two birefringent phase plates during their calibration.     

The ghost-gluon vertex in Hamiltonian Yang-Mills theory in Coulomb gauge

The Dyson-Schwinger equation for the ghost-gluon vertex of the Hamiltonian approach to Yang-Mills theory in Coulomb gauge is solved at one-loop level using as input the non-perturbative ghost and gluon propagators previously determined within the variational approach. The obtained ghost-gluon vertex is IR finite but IR enhanced compared to the bare one by 15%-25%, depending on the kinematical momentum regime.     

The method of the Poincaré map for compressional and torsional waves in composite rods

A generalized Poincaré map is introduced and used to find the compressional and torsional normal-mode frequencies and wave amplitudes of a one-dimensional rod composed by N coaxial cylinders of different length and radius. The method is approximately 100 times faster and more stable than the transfer matrix method. The Poincaré map method is used in a rod composed of two locally periodic systems, each one with a different length of the unit cell. This system can be used as an almost perfect mechanical noise filter.     

Renormalization of a gauge theory in a nonlinear gauge

We discuss renormalization of an O(3) gauge model with the gauge fixing term given by ℒ_g.f.=-1/ζ|(∂_μ-igA ₃ ^μ )W ^+μ|²-(1/2α)(∂A ³)². We utilize earlier results on the general theory of renormalization of gauge theories in quadratic gauges to prove multiplicative renormalizability of the theory together with a subtractive renormalization of gauge fixing and ghost terms. We show that this model has a double BRS invariance and that it is preserved under renormalization.     

Second order Hamiltonian formalism and constraints algebra for non-polynomial supergravities

The second order Hamiltonian formalism for a non-polynomial N = 1D = 10 supergravity coupled to super Yang-Mills theory is developed. This is done by starting from the first order canoncial covariant formalism on group manifold. The Hamiltonian, generator of time evolution, is found as a functional of the first class constraints of this coupled system. These contraints close the constraint algebra and they are the generators of all the Hamiltonian gauge symmetries.     

On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity

It is shown that all vacuum solutions of Einstein field equation with a positive cosmological constant are the solutions of a model of dS gauge theory of gravity. Therefore, the model is expected to pass the observational tests on the scale of solar systems and explain the indirect evidence of gravitational wave from the binary pulsars PSR1913+16.      

Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: Superfield formalism

We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D spacetime variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.      

Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge

We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss’ law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss’ law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schrödinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case.     

2维SU(NC)格点规范理论中矢量介子质量

用改进的格点哈密顿量和变分法,研究了2维SU(NC)规范场中矢量介子质量MV与夸克质量m和Wilson参数 的依赖关系．数值结果表明：对于NC =2、3、4、5、6、7, …,在标度窗口 内,MV/g与m的依赖关系近似为直线;但是矢量介子质量MV不明显依赖于Wilson参数 （这与夸克凝聚的情况不同）. 特别是,当 时, 本文的格点结果与Bhattacharya’s的连续理论强耦合相分析结果很好地一致, 而 的值十分接近Schwinger模型中的相应值.     

Generalized random phase approximation and gauge theories

Mean-field treatments of Yang-Mills theory face the problem of how to treat the Gauss law constraint. In this paper we try to face this problem by studying the excited states instead of the ground state. For this purpose we extend the operator approach to the Random Phase Approximation (RPA) well-known from nuclear physics and recently also employed in pion physics to general bosonic theories with a standard kinetic term. We focus especially on conservation laws, and how they are translated from the full to the approximated theories, demonstrate that the operator approach has the same spectrum as the RPA derived from the time-dependent variational principle, and give—for Yang-Mills theory—a discussion of the moment of inertia connected to the energy contribution of the zero modes to the RPA ground state energy. We also indicate a line of thought that might be useful to improve the results of the Random Phase Approximation.     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.     

General theory of renormalization of gauge theories in nonlinear gauges

We discuss the general theory of renormalization of unbroken gauge theories in the nonlinear gauges in which the gauge-fixing term is of the form We show that higher loop renormalization modifiesfα [A] to contain ghost terms of the form and show how the corresponding ghost terms are deduced fromfα [A, c, c] uniquely. We show that the theory can be renormalized while preserving a modified form of BRS invariance by multiplicative and independent renormalizations onA, c, g, η, ζ, τ. We briefly discuss the independence of the renormalized S-matrix from η,ζ, τ.     

Differential calculus and gauge transformations on a deformed space

We consider a formalism by which gauge theories can be constructed on noncommutative space time structures. The coordinates are supposed to form an algebra, restricted by certain requirements that allow us to realise the algebra in terms of star products. In this formulation it is useful to define derivatives and to extend the algebra of coordinates by these derivatives. The elements of this extended algebra are deformed differential operators. We then show that there is a morphism between these deformed differential operators and the usual higher order differential operators acting on functions of commuting coordinates. In this way we obtain deformed gauge transformations and a deformed version of the algebra of diffeomorphisms. The deformation of these algebras can be clearly seen in the category of Hopf algebras. The comultiplication will be twisted. These twisted algebras can be realised on noncommutative spaces and allow the construction of deformed gauge theories and deformed gravity theory. Dedicated to the 60th birthday of Prof. Obregon.     

Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type

We study purely nonlocal Hamiltonian structures for systems of hydrodynamic type. In the case of a semi-Hamiltonian system, we show that such structures are related to quadratic expansions of the diagonal metrics naturally associated with the system.