奇异拉氏量系统的整体量子正则对称性质

从奇异拉氏量系统相空间路径积分的量子化形式出发，导出了系统在增广相空间整体变换下的广义正则Ｗａｒｄ恒等式和量子水平的守恒荷，一般这些守恒荷有别于经典Ｎｏｅｔｈｅｒ荷．给出了在杨-Ｍｉｌｓ场论中的应用，找到了新守恒荷     

The Hamilton Cartan formalism for rth-order Lagrangians and the integrability of the KdV and modified KdV equations

The Hamilton Cartan formalism for rth order Lagrangians is presented in a form suited to dealing with higher-order conserved currents. Noether's Theorem and its converse are stated and Poisson brackets are defined for conserved charges. An isomorphism between the Lie algebra of conserved currents and a Lie algebra of infinitesimal symmetries of the Cartan form is established. This isomorphism, together with the commutativity of the Bäcklund transformations for the KdV and modified KdV equations, allows a simple geometric proof that the infinite collections of conserved charges for these equations are in involution with respect to the Poisson bracket determined by their Lagrangians. Thus, the formal complete integrability of these equations appears as a consequence of the properties of their Bäcklund transformations.It is noted that the Hamilton Cartan formalism determines a symplectic structure on the space of functionals determined by conserved charges and that, in the case of the KdV equation, the structure is the same as that given by Miura et al. [5].     

Local conserved currents for CPN σ-models

We present a new method to derive an infinite series of conserved local charges for the two-dimensional CP^N σ-models. The generating relation for the conservation laws is a couple of first-order nonlinear differential equations. The method displays transparently the connection of the local charges with nonlocal dynamical charges of CP^N models previously found.     

Tau-functions generating the conservation laws for generalized integrable hierarchies of KdV and affine toda type

For a class of generalized integrable hierarchies associated with affine (twisted or untwisted) Kac-Moody algebras, an explicit representation of their local conserved densities by means of a single scalar tau-function is deduced. This tau-function acts as a partition function for the conserved densities, which fits its potential interpretation as the effective action of some quantum system. The class consists of multi-component generalizations of the Drinfel'd-Sokolov and the two-dimensional affine Toda lattice hierarchies. The relationship between the former and the approach of Feigin, Frenkel and Enriquez to soliton equations of KdV and mKdV type is also discussed. These results considerably simplify the calculation of the conserved charges carried by the soliton solutions to the equations of the hierarchy, which is important to establish their interpretation as particles. By way of illustration, we calculate the charges carried by a set of constrained KP solitons recently constructed.     

The Limit of Noether Conserved Charges is the Number of Primary First-Class Constraints in a Constrained System

We discuss the stationarity of generator G for gauge symmetries in two directions.One is to the motion equations defined by total Hamiltonian H_T,and gives that the number of the independent coefficients in the generator G is not greater than the number of the primary first-class constraints,and the number of Noether conserved charges is not greater than that of the primary first-class constraints,too.The other is to the variances of canonical variables deduced from the generator G,and gives the variances of Lagrangian multipliers contained in extended Hamiltonian H_E.And a second-class constraint generated by a first-class constraint may imply a new first-class constraint which can be combined by introducing other second-class constraints.Finally,we supply two examples.One with three first-class constraints (two is primary and one is secondary) has two Noether conserved charges,and the secondary first-class constraint is combined by three second-class constraints which are a secondary and two primary second-class constraints.The other with two first-class constraints (one is primary and one is secondary) has one Noehter conserved charge.     

Flat Currents and Solutions of Sigma Model on Supercoset Targets with Z2m Grading

We find one parameter fiat currents of the sigma model on supercoset targets with Z2m grading given by Young satisfaction equations of motion and the Virasoro constraint. This means that one can generate a series of classical solutions from the original one. For these new solutions one can also construct fiat currents and conserved charges, which form the same set with the original one.     

Linearisation and potential symmetries of certain systems of diffusion equations

We consider systems of two pure one-dimensional diffusion equations that have considerable interest in Soil Science and Mathematical Biology. We construct non-local symmetries for these systems. These are determined by expressing the equations in a partially and wholly conserved form, and then by performing a potential symmetry analysis on those systems that can be linearised. We give several examples of such systems, and in a specific case we show how linearising and hodograph-type mappings can lead to new solutions of the diffusion system.     

Hopf Solitons and Area-Preserving Diffeomorphisms of the Sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S ². The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S ². We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.     

The Transformation Properties at the Quantum Level in Field Theories for a Gauge-Invariant System with a Higher-Order Lagrangian

Based on the configuration-space generating functional of the Green functions for the gauge-invariant system in higher-order derivatives theories, the equations of the transformation properties at the quantum level have been derived. It follows that the sufficient conditions are found which implies that there exists the conservation laws and the expressions of the quantal conserved laws are also given. Applying the results to the non-Abelian Chern-Simons higher-order derivatives theories, the quantal BRST conserved charge and other conserved charges are found, the transformation properties of the conformal transformation at the quantum level is discussed, the quantal conserved angular momentum is derived, it is pointed out that fractional spin in this system may be also preserved in quantum theories. But the connection between the symmetries and conservation laws in classical theories are not always preserved in quantum theories.     

Electrodynamics of Balanced Charges

We introduce here a new “neoclassical” electromagnetic (EM) theory in which elementary charges are represented by wave functions and individual EM fields to account for their EM interactions. We call so defined charges balanced or “b-charges”. We construct the EM theory of b-charges (BEM) based on a relativistic field Lagrangian and show that: (i) the elementary EM fields satisfy the Maxwell equations; (ii) the Newton equations with the Lorentz forces hold approximately when b-charges are well separated and move with non-relativistic velocities. When the BEM theory is applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the Schrodinger model with desired accuracy. An important feature of the theory is a mechanism of elementary EM energy absorption established for retarded potentials.     

弱非完整系统Mei对称性导致的新型精确和近似守恒量

研究弱非完整系统Lagrange方程的Mei对称性导致的一种结构方程和新型精确以及近似守恒量. 首先建立系统的Lagrange方程. 其次在群的无限小变换下, 给出了弱非完整系统及其一次近似系统Mei对称性的定义和判据, 然后得到了Mei对称性导致的新型结构方程、 新型精确和近似守恒量的表达式. 最后, 举例研究系统的精确新型守恒量和近似新型守恒量问题. 关键词： 弱非完整系统 Mei对称性 新型结构方程 新型守恒量     

Scalar-vector topological soliton

We present classical scalar-vector equations which admit soliton solutions in three space dimensions. Exact spherical solutions are obtained which are everywhere regular and resemble charged particles of finite self-energy. The corresponding 4-current is identically conserved and leads to quantized charges. The scale of the soliton is unique and determined by boundary conditions, which also ensure its topological stability.     

Wave-Corpuscle Mechanics for Electric Charges

It is well known that the concept of a point charge interacting with the electromagnetic (EM) field has a problem. To address that problem we introduce the concept of wave-corpuscle to describe spinless elementary charges interacting with the classical EM field. Every charge interacts only with the EM field and is described by a complex valued wave function over the 4-dimensional space time continuum. A system of many charges interacting with the EM field is defined by a local, gauge and Lorentz invariant Lagrangian with a key ingredient—a nonlinear self-interaction term providing for a cohesive force assigned to every charge. An ideal wave-corpuscle is an exact solution to the Euler-Lagrange equations describing both free and accelerated motions. It carries explicitly features of a point charge and the de Broglie wave. Our analysis shows that a system of well separated charges moving with nonrelativistic velocities are represented accurately as wave-corpuscles governed by the Newton equations of motion for point charges interacting with the Lorentz forces. In this regime the nonlinearities are “stealthy” and don’t show explicitly anywhere, but they provide for the binding forces that keep localized every individual charge. The theory can also be applied to closely interacting charges as in hydrogen atom where it produces discrete energy spectrum.     

Nielsen方程Mei对称性导致的一种新型守恒量

研究完整系统Nielsen方程Mei对称性导致的一种新型守恒量.在群的无限小变换下,由Nielsen方程Mei对称性的定义和判据,得到完整系统Nielsen方程Mei对称性导致的新型结构方程和新型守恒量.举例说明结果的应用. 关键词： Nielsen方程 Mei对称性 新型结构方程 新型守恒量     

Charged black holes on Kaluza–Klein bubbles

We construct exact solutions of the Einstein–Maxwell field equations in five dimensions, which describe general configurations of charged and static black holes sitting on a Kaluza–Klein bubble. More specifically we discuss the configurations describing two black holes sitting on a Kaluza–Klein bubble and also the general charged static black Saturn balanced by a Kaluza–Klein bubble. A straightforward extension of the solution-generating technique leads to a new solution describing the charged static black Saturn on the Taub-bolt instanton. We compute the conserved charges and investigate some of the thermodynamic properties of these systems.     

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system.On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation,the determining equations,the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed.The criterions of Mei symmetries,weak Mei symmetries and strong Mei symmetries of the system are given.New types of conserved quantities,i.e.the Mei symmetrical conserved quantities,the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system,are obtained.Then,a deduction of the first-order nonholonomic system is discussed.Finally,two examples are given to illustrate the application of the method and then the results.     

A type of new conserved quantity deduced from Mei symmetry for Appell equations in a holonomic system with unilateral constraints

A type of new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints is investigated.The expressions of new structural equation and new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints expressed by Appell functions are obtained.An example is given to illustrate the application of the results.     

Form factors,deformed Knizhnik-Zamolodchikov equations and finite-gap integration

We study the limit of asymptotically free massive integrable models in which the algebra of nonlocal charges turns into affine algebra. The form factors of fields in that limit are described by KZ equations on level 0. We show the limit to be connected with finite-gap integration of classical integrable equations.     

A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints

<正>A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints is investigated.Nielsen equations and differential equations of motion for the holonomic mechanical system with unilateral constraints are established.The definition and the criterion of Mei symmetry for Nielsen equations in the holonomic systems with unilateral constraints under the infinitesimal transformations of Lie group are also given.The expressions of the structural equation and a type of new conserved quantity of Mei symmetry for Nielsen equations in the holonomic system with unilateral constraints are obtained.An example is given to illustrate the application of the results.