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Noether’s Theorem on Non-Trivial Manifolds Daniel Martin Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom 13/03/2014 Noether’s theorem has been used to great success throughout many areas of physics, and has been one of the main generators of new research areas.
We present a functor between the category of smooth manifolds equipped with diffeomorphisms (or local diffeomorphisms) and the category of symplectic manifolds equipped with symplectomorphisms for which the object assignment consists of associating to a space its cotangent bundle.
GENERAL RELATIVITY LORENTZ GROUP QUANTUM FIELD THEORY (Operator-valued fields on R 4obeying certain Lorentzinvariant PDE’s and commutation relationships, acting on an abstract Hilbert space) (3+1-dimensional pseudo-Riemannian manifolds with tensor fields obeying PDE’s of, say, Einstein-Maxwell theory with perfect fluid component) SU(2) Specialize LIE GROUPS LIE ALGEBRAS DIFFERENTIAL OPERATORS ALGEBRAS LINEAR OPERATORS Define linear vector mappings TRIPLE FIELDS Add 4th binary op.
The spatial dimension is typically described by M , an n dimensional manifold without boundary with bordisms of n-manifolds describing the evolution of this system.
See the notes regarding the low pressure switch above We can supply manifolds with M24 outlets as needed by some teams.
3 An Application to Questions of Uniqueness It was Borel who first asked whether manifolds can be described.