The dirac-schwinger covariance condition in classical field theory

A straightforward derivation of the Dirac-Schwinger covariance condition is given within the framework of classical field theory. The crucial role of the energy continuity equation in the derivation is pointed out. The origin of higher order derivatives of delta function is traced to the presence of higher order derivatives of canonical coordinates and momenta in the energy density functional.     

Chaos feature of test particle in the gravitational field with a quadrupole

In this paper we investigate the dynamics of a test particle in the gravitational field with a quadrupole. By constructing Poincaré sections for different values of the parameters and initial conditions, we find a chaotic evolution. From these Poincaré sections, we further confirm that the chaotic evolution of the test particle originates from the quadrupole.     

Topological field patterns in the Yang-Mills theory

We present a formalism where the topological configurations of pure Yang-Mills theory are characterised using gauge fields alone. Here, we obtain an expression for the charges of these topologicalSO(3) gauge field configurations in terms of the Abelian vector potentials. In this formalism we analyse the ’t Hooft-Polyakov monopole solution.     

Chaos in a gravitational field with dipoles

In this paper we investigate the dynamics of a test particle in the gravitational field with dipoles. At first we study the gravitational potential by numerical simulations, we find that, for appropriate parameters, there are two different cases in the potential curve: one is the one-well case with a stable critical point, and the other is the three-well case with three stable critical points and two unstable critical points. By performing Poincare sections for different values of the parameters and initial conditions, we find a regular motion and a chaotic motion. From these Poincar6 sections,we further confirm that the chaotic motion of the test particle originates mainly from the dipoles.     

Functional determinants in euclidean Yang-Mills theory

We study functional determinants entering the path integral for topologically non-trivial sectors of Euclidean SU(2) Yang-Mills theory and we derive some results in exact closed form.This work is supported through funds provided by the US Department of Energy (DOE) under Contract EY-76-C-02-3069 and by the National Science Foundation through funds provided under Contract PHY 79-16812     

Large-N reduction in the continuum three-dimensional Yang-Mills theory

Numerical and theoretical evidence leads us to propose the following: Three-dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase transition on a torus of side l=l(c). For l>l(c) the planar limit is l independent, as expected of a noninteracting string theory. We expect the situation in four dimensions to be similar.     

电场中里德伯原子动力学性质的半经典理论研究

利用闭合轨道理论和Poincaré截面两种方法研究了鞍点附近电场中高里德伯态Li原子的动力学性质.由于原子实的作用,体系是混沌的,闭合轨道和周期轨道在混沌体系中并存,但二者在Poincaré截面上的反映是不同的.讨论了两种半经典理论在研究混沌体系时的联系,得到了仅靠闭合轨道理论得不到的信息. 关键词： Poincaré截面 回归谱 Stark效应     

Electric vortex lines from the Yang-Mills theory

We develop the dynamics of an unstable Yang-Mills field mode previously found by us. We argue that this unstable mode corresponds to the transition to a state where electric vortex lines are created.     

On the dynamics of the Szekeres system

The gravitational Szekeres differential system is completely integrable with two rational first integrals and an additional analytical first integral. We describe the dynamics of the Szekeres system when one of these two rational first integrals is negative, showing that all the orbits come from the infinity of ${\mathbb{R}}^4$ and go to infinity.     

The β-function in supersymmetric Yang-Mills theory

We show by means of the Adler-Bardeen theorem how to calculate the two-loop β function from a one-loop calculation of the superconformal anomaly in a supersymmetric gauge theory with arbitrary superpotential. The N = 2 and N = 4 cases are also briefly discussed.     

Gluon cluster solution in effective Yang-Mills theory

A finite-energy classical solution in effective Yang-Mills theory specified by a nonstandard Lagrangian is obtained. The effect of vacuum polarization on the formation of gluon clusters is discussed.     

Liquid-crystal defects and confinement in Yang-Mills theory

It has been shown that, in the Landau gauge of the SU(2) Yang-Mills theory, the residual global symmetry supports the existence of topological vortices which resemble disclination defects in nematic liquid crystals and Alice (half-quantum) vortices in superfluid ³He in the A-phase. The theory also possesses half-integer and integer-charged monopoles, which are analogous to the point-like defects in nematic crystal and in liquid helium. We argue that the deconfinement phase transition in the Yang-Mills theory in the Landau gauge is associated with the proliferation of these vortices and/or monopoles. The text was submitted by the author in English.     

Dynamical mass generation in three-dimensional Yang-Mills theory

We calculate an effective potential for three-dimensional Yang-Mills theory to two loops. The result implies that a gauge invariant part of the field strength has a non-zero vacuum expectation value, φ. The two-point function of this field, calculated to one loop, shows that two polarization states propagate with a mass proportional to √φ. In contrast to the usual Higgs mechanism the remaining degrees of freedom do not propagate. This dynamical generation of a “glueball” mass renders the already ultraviolet finite theory infrared finite and stabilizes vortices associated with the centre of the group.     

Infrared divergence cancellation in pure Yang-Mills theory

Virtual and real corrections to massless external lines in pure Yang-Mills theory are considered in order to look for general features of the infrared divergence cancellation. Use of the Ward identities and sums over transverse polarization states give rise to terms formally corresponding to real ghost emission, cancelling ghost loop singularities, and to a factorisation of the hard narrow single gauge boson emission. Other virtual corrections are examined in the soft region and a graph cancellation is also found. An illustrative explicit calculation of scattering of a gauge particle in an external scalar potential, including hard narrow angle emission is presented.     

Hamilton’s theory of turns and a new geometrical representation for polarization optics

Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics. While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the solid angle on the Poincaré sphere, is established.     

A compensating functional method in the massive Yang-Mills theory

In the massive and massless Yang-Mills theories the generating functional (the S-matrix) independence of the gauge parameter is provided on the mass shell without introducing an extra degree of freedom (gauge group integration).     

Yang-Mills theory in three dimensions as a quantum gravity theory

We perform the dual transformation of theYang-Mills theory in three dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but which is embedded into a flat 6-dimensional space [for the SU(2) gauge group]. In the continuum limit, the theory can be reformulated in terms of 6-component gauge-invariant scalar fields having the meaning of the external coordinates of the dual lattice sites. These 6-component fields induce a metric and a curvature of the 3-dimensional dual-color space. The Yang-Mills theory can also be rewritten as a quantum gravity theory with the Einstein-Hilbert action but with a purely imaginary Newton constant plus a homogeneous “ether” term. The theory can be formulated in a gauge-invariant and local form without explicit color degrees of freedom.     

Observables in topological Yang-Mills theory and the Gribov problem

The origin of the nontriviality of observables in topological Yang-Mills theory is discussed from the viewpoint that BRST transformation is the exterior derivative. We show that the appearance of singularities due to the Gribov problem makes the Donaldson polynomials cohomologically nontrivial.