Two Dimensional Quantum Chromodynamics as the Limit of Higher Dimensional Theories

We define pure gauge $QCD$ on an infinite strip of width $L$. Techniques similar to those used in finite $TQCD$ allow us to relate $3D$-observables to pure $QCD_2$ behaviors. The non triviality of the L \arrow 0 limit is proven and the generalization to four dimensions described. The glueball spectrum of the theory in the small width limit is calculated and compared to that of the two dimensional theory.Comment: 12 pages written in LaTeX, figure available from the authors, preprint Univ. of Valencia, FTUV/94-4

An intrinsic characterization of 2+2 warped spacetimes

We give several equivalent conditions that characterize the 2+2 warped spacetimes: imposing the existence of a Killing-Yano tensor $A$ subject to complementary algebraic restrictions; in terms of the projector $v$ (or of the canonical 2-form $U$) associated with the 2-planes of the warped product. These planes are principal planes of the Weyl and/or Ricci tensors and can be explicitly obtained from them. Therefore, we obtain the necessary and sufficient (local) conditions for a metric tensor to be a 2+2 warped product. These conditions exclusively involve explicit concomitants of the Riemann tensor. We present a similar analysis for the conformally 2+2 product spacetimes and give an invariant classification of them. The warped products correspond to two of these invariant classes. The more degenerate class is the set of product metrics which are also studied from an invariant point of view.Comment: 18 pages; submitted to Class. Quantum Grav

Obtaining the Weyl tensor from the Bel-Robinson tensor

The algebraic study of the Bel-Robinson tensor proposed and initiated in a previous work (Gen. Relativ. Gravit. {\bf 41}, see ref [11]) is achieved. The canonical form of the different algebraic types is obtained in terms of Bel-Robinson eigen-tensors. An algorithmic determination of the Weyl tensor from the Bel-Robinson tensor is presented.Comment: 21 page

A topological charge selection rule for phase singularities

We present an study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.Comment: 4 pages, 3 figure

Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.Comment: 19 pages; a reference adde

Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we explore the possibilities of the generalization of the previous framework to the quantum limit.Comment: 18 pages; submitted to Physica