Book contents
- Frontmatter
- Contents
- The network
- Preface
- The constraint algebra of higher dimensional Chern-Simons theories
- Nonrelativistic Chern-Simons vortices from the constrained Hamiltonian formalism
- Classical solutions of gravitating Chern-Simons electrodynamics
- Exponentially localised instantons in a hierarchy of Higgs models
- Obstructions to ganging WZ terms: a symplectic curiosity
- Global aspects of symmetries in sigma models with torsion
- Canonical structure of the non-linear σ-model in a polynomial formulation
- A manifestly gauge-invariant approach to quantum theories of gauge fields
- On the Hamiltonian formulation of higher dimensional Chern-Simons gravity
- An Example of Loop Quantization
- Gauge fixing in constrained systems
- Light-cone formulation of gauge theories
- Hamiltonian constraints and Dirac observables
- Gauging kinematical and internal symmetry groups for extended systems
- On the harmonic interaction of three relativistic point particles
- Non existence of static multi-black-hole solutions in 2+1 dimensions
- Spherically symmetric gravity and the notion of time in general relativity
- Canonical decomposition of Belinskii-Zakharov one-soliton solutions
- Hamiltonian reduction and the R-matrix of the Calogero model
- Intrinsic approach to the Legendre transformation in super-mechanics
- Field-antifield description of anomalous theories
- Transfer matrix quantization of general relativity, and the problem of time
- The W3-particle
- Pure geometrical approach to singular Lagrangians with higher derivatives
- Dirac versus reduced phase space quantization
- Classical and quantum aspects of degenerate metric fields
- BRST-antibracket cohomology in 2d conformal gravity
- Quantisation of 2 + 1 gravity for g = 1 and g = 2
- Geometry and dynamics with time-dependent constraints
- Collective coordinates and BRST transformations or Gauge theories without gauge fields
- Geometry of fermionic constraints in superstring theories
- BRST and new superstring states
- Generalized canonical quantization of gauge theories with polarized second–class constraints
- Radiation field on superspace
- Participants
The W3-particle
Published online by Cambridge University Press: 05 November 2011
- Frontmatter
- Contents
- The network
- Preface
- The constraint algebra of higher dimensional Chern-Simons theories
- Nonrelativistic Chern-Simons vortices from the constrained Hamiltonian formalism
- Classical solutions of gravitating Chern-Simons electrodynamics
- Exponentially localised instantons in a hierarchy of Higgs models
- Obstructions to ganging WZ terms: a symplectic curiosity
- Global aspects of symmetries in sigma models with torsion
- Canonical structure of the non-linear σ-model in a polynomial formulation
- A manifestly gauge-invariant approach to quantum theories of gauge fields
- On the Hamiltonian formulation of higher dimensional Chern-Simons gravity
- An Example of Loop Quantization
- Gauge fixing in constrained systems
- Light-cone formulation of gauge theories
- Hamiltonian constraints and Dirac observables
- Gauging kinematical and internal symmetry groups for extended systems
- On the harmonic interaction of three relativistic point particles
- Non existence of static multi-black-hole solutions in 2+1 dimensions
- Spherically symmetric gravity and the notion of time in general relativity
- Canonical decomposition of Belinskii-Zakharov one-soliton solutions
- Hamiltonian reduction and the R-matrix of the Calogero model
- Intrinsic approach to the Legendre transformation in super-mechanics
- Field-antifield description of anomalous theories
- Transfer matrix quantization of general relativity, and the problem of time
- The W3-particle
- Pure geometrical approach to singular Lagrangians with higher derivatives
- Dirac versus reduced phase space quantization
- Classical and quantum aspects of degenerate metric fields
- BRST-antibracket cohomology in 2d conformal gravity
- Quantisation of 2 + 1 gravity for g = 1 and g = 2
- Geometry and dynamics with time-dependent constraints
- Collective coordinates and BRST transformations or Gauge theories without gauge fields
- Geometry of fermionic constraints in superstring theories
- BRST and new superstring states
- Generalized canonical quantization of gauge theories with polarized second–class constraints
- Radiation field on superspace
- Participants
Summary
Abstract
We show that W3 is the algebra of symmetries of the “rigid-particle”, whose action is given by the integrated extrinsic curvature of its world line. This is easily achived by showing that its equation of motion can be written in terms of the Boussinesq operator. We also show how to obtain the equations of motion of the standard relativistic particle provided it is consistent to impose the “zero-curvature gauge”, and comment about its connection with the KdV operator.
Introduction
The geometrical interpretation of W-type symmetries has attracted the attention of many mathematical physicists in recent years. Although a plethora of interesting results are now at our disposal it is commonly agreed that we have not yet a complete understanding of the underlying geometry. It is clear that simple mechanical systems enjoying W symmetry could be an unvaluable tool in this difficult task. On one hand they could provide us with some geometrical and/or physical interpretation for W-transformations (W-morphisms), while on the other hand they could give us some hints about which are the relevant structures associated with W-gravity - the paradigmatic example being provided by the standard relativistic particle and difTeomorphism invariance (W2).
It is well known by now the connection between W-morphisms and the extrinsic geometry of curves and surfaces [1]. Therefore, it seems natural to look for a W-particle candidate among the geometrical actions depending on the extrinsic curvature.
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- Information
- Geometry of Constrained Dynamical Systems , pp. 220 - 228Publisher: Cambridge University PressPrint publication year: 1995