4,622 research outputs found
About Symmetries in Physics
The goal of this introduction to symmetries is to present some general ideas,
to outline the fundamental concepts and results of the subject and to situate a
bit the following lectures of this school. [These notes represent the write-up
of a lecture presented at the fifth ``Seminaire Rhodanien de Physique: Sur les
Symetries en Physique" held at Dolomieu (France), 17-21 March 1997. Up to the
appendix and the graphics, it is to be published in "Symmetries in Physics",
F.Gieres, M.Kibler,C.Lucchesi and O.Piguet, eds. (Editions Frontieres, 1998).]Comment: Latex, 42 pages, 4 figure
Twistor Theory and Differential Equations
This is an elementary and self--contained review of twistor theory as a
geometric tool for solving non-linear differential equations. Solutions to
soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or
Sine-Gordon arise from holomorphic vector bundles over T\CP^1. A different
framework is provided for the dispersionless analogues of soliton equations,
like dispersionless KP or Toda system in 2+1 dimensions. Their
solutions correspond to deformations of (parts of) T\CP^1, and ultimately to
Einstein--Weyl curved geometries generalising the flat Minkowski space. A
number of exercises is included and the necessary facts about vector bundles
over the Riemann sphere are summarised in the Appendix.Comment: 23 Pages, 9 Figure
A Simple Introduction to Grobner Basis Methods in String Phenomenology
In this talk I give an elementary introduction to the key algorithm used in
recent applications of computational algebraic geometry to the subject of
string phenomenology. I begin with a simple description of the algorithm itself
and then give 3 examples of its use in physics. I describe how it can be used
to obtain constraints on flux parameters, how it can simplify the equations
describing vacua in 4d string models and lastly how it can be used to compute
the vacuum space of the electroweak sector of the MSSM.Comment: 13 pages, Prepared for Mathematical Challenges in String
Phenomenology, ESI Vienna, Austria, Oct 6-15, 200
Lagrange Anchor and Characteristic Symmetries of Free Massless Fields
A Poincar\'e covariant Lagrange anchor is found for the non-Lagrangian
relativistic wave equations of Bargmann and Wigner describing free massless
fields of spin in four-dimensional Minkowski space. By making use of
this Lagrange anchor, we assign a symmetry to each conservation law and perform
the path-integral quantization of the theory
Extended 2d generalized dilaton gravity theories
We show that an anomaly-free description of matter in (1+1) dimensions
requires a deformation of the 2d relativity principle, which introduces a
non-trivial center in the 2d Poincare algebra. Then we work out the reduced
phase-space of the anomaly-free 2d relativistic particle, in order to show that
it lives in a noncommutative 2d Minkowski space. Moreover, we build a Gaussian
wave packet to show that a Planck length is well-defined in two dimensions. In
order to provide a gravitational interpretation for this noncommutativity, we
propose to extend the usual 2d generalized dilaton gravity models by a specific
Maxwell component, which gauges the extra symmetry associated with the center
of the 2d Poincare algebra. In addition, we show that this extension is a high
energy correction to the unextended dilaton theories that can affect the
topology of space-time. Further, we couple a test particle to the general
extended dilaton models with the purpose of showing that they predict a
noncommutativity in curved space-time, which is locally described by a Moyal
star product in the low energy limit. We also conjecture a probable
generalization of this result, which provides a strong evidence that the
noncommutativity is described by a certain star product which is not of the
Moyal type at high energies. Finally, we prove that the extended dilaton
theories can be formulated as Poisson-Sigma models based on a nonlinear
deformation of the extended Poincare algebra.Comment: 21 pages, IOP LaTeX2e preprint classfile, Improved discussions, Minor
corrections, More didactic, More self-contained, New results concerning
noncommutativity in curved space-time, Accepted for publication in Classical
and Quantum Gravity on 02 Jul 200
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