自对偶场与规范场相互作用理论的Faddeev－Jackiw量子化

本文采用Ｆａｄｄｅｅｖ－Ｊａｃｋｉｗ量子化方法，讨论了二维时空中一种自对偶场与规范场的相互作用理论．通过与Ｄｉｒａｃ方法的比较，建立了这两种方法的等价性     

Order parameters and boundary effects in U(1) lattice gauge theory

We show that, independently of the boundary conditions, the two phases of the 4-dimensional compact U(1) lattice gauge theory can be characterized by the presence or absence of an “infinite” current network, with an appropriate definition of “infinite” network takes values 0 or 1 in the cold and hot phase, respectively. It thus constitutes a very efficient order parameter, which allows one to determine the transition region at low computational cost. In addition, for open and fixed boundary conditions we address the question of the impact of inhomogeneities and give examples of the reappearance of an energy gap already at moderate lattice sizes.     

Off-diagonal long-range order and the Meissner effect

We provide a general, model-independent, derivation of the Meissner effect, on the basis of assumptions of off-diagonal long-range order (ODLRO) and gauge covariance of the second kind. This is an exact result that is independent of the microscopic mechanism responsible for the ordering, and so is applicable both to high- and low-T _c superconductors.     

The boundary rigidity problem in the presence of a magnetic field

For a compact Riemannian manifold with boundary, endowed with a magnetic potential α, we consider the problem of restoring the metric g and the magnetic potential α from the values of the Mañé action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Mañé action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of α.For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on α. We also show injectivity and stability for g and α in a generic class G including real analytic ones.For the nonlinear problem, we show rigidity for real analytic simple (g,α), rigidity for metrics in a given conformal class, and locally, near any (g,α)∈G. We also show that simple magnetic systems on two-dimensional manifolds are always rigid.     

Operator matrices on topological vector spaces

A series of basic summability results are established for matrices of linear and some nonlinear operators between topological vector spaces.     

Compactness theorems for coupled Yang-Mills fields

In this paper, we consider coupled Yang-Mills fields on vector bundle E over compact Riemannian manifold M. Under appropriate conditions on the curvature and the Higgs field, two compactness theorems are proved.     

Maxwell–Dirac Equations in Four-Dimensional Minkowski Space

Abstract

I derive the global existence and asymptotic behavior of small amplitude solutions to the system of massive coupled classical Maxwell–Dirac equations in the four-dimensional Minkowski space. Because the physically defined energy of the system is not positive definite, I transform it into an equivalent system of Maxwell–Klein–Gordon equations, which I study with a method based on gauge invariant energy estimates and geometric properties of the equations.     

The Balian–Low theorem and noncommutative tori

We point out a link between the theorem of Balian and Low on the non-existence of well-localized Gabor–Riesz bases and a constant curvature connection on projective modules over noncommutative tori.     

Obtaining the Gauge Invariant Kinetic Term for a SU(n) U ⊗ SU(m) V Lagrangian

We propose a generalized way to formally obtain the gauge invariance of the kinetic part of a field Lagrangian over which a gauge transformation ruled by an SU(n) _U ⊗ SU(m) _V coupling symmetry is applied. As an illustrative example, we employ such a formal construction for reproducing the standard model Lagrangian. This generalized formulation is supposed to contribute for initiating the study of gauge transformation applied to generalized SU(n) _U ⊗ SU(m) _V symmetries as well as for complementing an introductory study of the standard model of elementary particles.