## Geometric structures in nonlinear physicsVOLUME 26 of INTERDISCIPLINARY MATHEMATICS, series expounding mathematical methodology in Physics & Engineering. TOPICS: Differential & Riemannian Geometry; Theories of Vorticity Dynamics, Einstein-Hilbert Gravitation, Colobeau-Rosinger Generalized Function Algebra, Deformations & Quantum Mechanics of Particles & Fields. Ultimate goal is to develop mathematical framework for reconciling Quantum Mechanics & concept of Point Particle. New ideas for researchers & students. Order: Math Sci Press, 53 Jordan Road, Brookline, MA 02146. (617) 738-0307. |

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### Contents

PREFACE | 1 |

SOME RESEARCH DIRECTIONS IN LIE PSEUDOGROUPS 6 | 6 |

The variational problem associated with LieSpencer 1 | 11 |

Copyright | |

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### Common terms and phrases

affine connection associated Brookline Calculus of Variations called canonical commutation relations Cartan form Classical Mechanics Colombeau compute conservation laws constraints coordinate system covariant derivative Current Algebra curve defined Definition Deformation Theory denote diffeomorphisms differential forms Differential Geometry dual dynamical system exterior derivative exterior differential system Field Equations finite Fluid Equations fluid flow Fluid Mechanics following condition following form geometric structure Hamiltonian Hermann Hilbert space infinite dimensional Lie integral Interdisciplinary Mathematics involve Lagrangian field theories Levi-Civita Lie algebra Lie derivative Lie group Lie Group Theory Lie pseudogroups linear differential operator Math Sci Press matrix moving frame nonlinear partial differential equations Phys physicists Poisson Bracket Proof pseudogroup quantization quantum field theory quantum mechanics real numbers real-valued function renormalization Riemannian geometry Riemannian manifold Riemannian metric satisfying the following Spencer Suppose symmetric symplectic Theorem variational problem variational system vector bundle vector fields vector space vorticity Yang-Mills