Classical integrability of chiral QCD2QCD_{2} and classical curves

In this letter, classical chiral $QCD_{2}$ is studied in the lightcone gauge $A_{-}=0$. The once integrated equation of motion for the current is shown to be of the Lax form, which demonstrates an infinite number of conserved quantities. Specializing to gauge group SU(2), we show that solutions to the classical equations of motion can be identified with a very large class of curves. We demonstrate this correspondence explicitly for two solutions. The classical fermionic fields associated with these currents are then obtained.Comment: Final version to appear in Mod. Phys. Lett. A. A reference and two footnotes added. 6 pages revte

Quantum cosmological Friedman models with a massive Yang-Mills field

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a massive Yang-Mills field. The resolution is achieved by first solving the free eigenvalue problem for the gravitational field and then the constrained eigenvalue problem for the Yang-Mills field. In the latter case the mass of the Yang-Mills field assumes the role of the eigenvalue.Comment: 16 pages, v3: typos corrected, final version, to appear in CQ

A Comment on Junction and Energy Conditions in Thin Shells

This comment contains a suggestion for a slight modification of Israel's covariant formulation of junction conditions between two spacetimes, placing both sides on equal footing with normals having uniquely defined orientations. The signs of mass energy densities in thin shells at the junction depend not only on the orientations of the normals and it is useful therefore to discuss the sign separately. Calculations gain in clarity by not choosing the orientations in advance. Simple examples illustrate our point and complete previous classifications of spherical thin shells in spherically symmetric spacetimes relevant to cosmology.Comment: (Tex file + PS file with a figure) Tex errors were correcte

Geometric Properties of Static EMdL Horizons

We study non-degenerate and degenerate (extremal) Killing horizons of arbitrary geometry and topology within the Einstein-Maxwell-dilaton model with a Liouville potential (the EMdL model) in d-dimensional (d>=4) static space-times. Using Israel's description of a static space-time, we construct the EMdL equations and the space-time curvature invariants: the Ricci scalar, the square of the Ricci tensor, and the Kretschmann scalar. Assuming that space-time metric functions and the model fields are real analytic functions in the vicinity of a space-time horizon, we study behavior of the space-time metric and the fields near the horizon and derive relations between the space-time curvature invariants calculated on the horizon and geometric invariants of the horizon surface. The derived relations generalize the similar relations known for horizons of static four and 5-dimensional vacuum and 4-dimensional electrovacuum space-times. Our analysis shows that all the extremal horizon surfaces are Einstein spaces. We present necessary conditions for existence of static extremal horizons within the EMdL model.Comment: 10 page

Geometrical classification of Killing tensors on bidimensional flat manifolds

Valence two Killing tensors in the Euclidean and Minkowski planes are classified under the action of the group which preserves the type of the corresponding Killing web. The classification is based on an analysis of the system of determining partial differential equations for the group invariants and is entirely algebraic. The approach allows to classify both characteristic and non characteristic Killing tensors.Comment: 27 pages, 20 figures, pictures format changed to .eps, typos correcte

The Embedding of Schwarzschild in Braneworld

The braneworlds models were inspired partly by Kaluza-Klein's theory, where both the gravitational and the gauge fields are obtained from the geometry of a higher dimensional space. The positive aspects of these models consist in perspectives of modifications it could bring in to particle physics, such as: unification in a TeV scale, quantum gravity in this scale and deviation of Newton's law for small distances. One of the principles of these models is to suppose that all space-times can be embedded in a bulk of higher dimension. The main result in these notes is a theorem showing a mathematical inconsistency of the Randall-Sundrum braneworld model, namely that the Schwarzschild space-time cannot be embedded locally and isometrically in a five dimensional bulk with constant curvature,(for example AdS-5). From the point of view of semi-Riemannian geometry this last result represents a serious restriction to the Randall-Sundrum's braneworld model.Comment: Published in the Int. J. Theor. Phys, 200

Helicity-Rotation-Gravity Coupling for Gravitational Waves

The consequences of spin-rotation-gravity coupling are worked out for linear gravitational waves. The coupling of helicity of the wave with the rotation of a gravitational-wave antenna is investigated and the resulting modifications in the Doppler effect and aberration are pointed out for incident high-frequency gravitational radiation. Extending these results to the case of a gravitomagnetic field via the gravitational Larmor theorem, the rotation of linear polarization of gravitational radiation propagating in the field of a rotating mass is studied. It is shown that in this case the linear polarization state rotates by twice the Skrotskii angle as a consequence of the spin-2 character of linear gravitational waves.Comment: 11 pages, no figures, accepted for publication in Phys. Rev. D; v2: a few minor typos correcte

Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method

We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t=1000m. The principle features of our method are i) the use of a lattice to record the geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM equations to the lattice and iii) the use of the Bianchi identities to assist in the computation of the curvatures. No other special techniques are used. The evolution is unconstrained and the ADM equations are used in their standard form.Comment: 47 pages including 26 figures, plain TeX, also available at http://www.maths.monash.edu.au/~leo/preprint

Mass Hierarchy, Mixing, CP-Violation and Higgs Decay---or Why Rotation is Good for Us

The idea of a rank-one rotating mass matrix (R2M2) is reviewed detailing how it leads to ready explanations both for the fermion mass hierarchy and for the distinctive mixing patterns between up and down fermion states, which can be and have been tested against experiment and shown to be fully consistent with existing data. Further, R2M2 is seen to offer, as by-products: (i) a new solution of the strong CP problem in QCD by linking the theta-angle there to the Kobayashi-Maskawa CP-violating phase in the CKM matrix, and (ii) some novel predictions of possible anomalies in Higgs decay observable in principle at the LHC. A special effort is made to answer some questions raised.Comment: 47 pages, 9 figure

On the Invariant Theory of Weingarten Surfaces in Euclidean Space

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal surfaces, surfaces of constant mean curvature and surfaces of constant Gauss curvature.Comment: 16 page