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Un-reduction in field theory.

Alexis Arnaudon1, Marco Castrillón López2, Darryl D Holm1

  • 11Department of Mathematics, Imperial College, London, SW7 2AZ UK.

Letters in Mathematical Physics
|January 23, 2018
PubMed
Summary
This summary is machine-generated.

A novel covariant un-reduction procedure is extended from classical mechanics to field theory. This method advances shape matching for complex images and explores nonlinear models and hyperbolic curve flows.

Keywords:
Classical field theoryCurve matchingLagrange–Poincaré reductionSigma models

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Area of Science:

  • Theoretical physics
  • Mathematical physics

Background:

  • Classical mechanics previously utilized an un-reduction procedure.
  • Covariant field theory offers a framework for describing fundamental forces and particles.

Purpose of the Study:

  • To extend the un-reduction procedure to covariant field theory.
  • To apply this new procedure to shape matching problems.
  • To explore applications in nonlinear models and hyperbolic curve flows.

Main Methods:

  • Extension of the un-reduction procedure to the covariant field theory framework.
  • Application of the procedure to image shape matching with multiple variables.
  • Investigation of nonlinear [Formula: see text]-models and hyperbolic curve flows.

Main Results:

  • Successful extension of the un-reduction procedure to covariant field theory.
  • Demonstrated utility of the procedure for shape matching of multi-variable images.
  • Exploration of potential applications in advanced mathematical physics.

Conclusions:

  • The covariant un-reduction procedure is a powerful tool for extending classical mechanics concepts to field theory.
  • This methodology offers new avenues for image analysis and the study of nonlinear phenomena.