Introduction 1. A general setting and a motivating example 2. Weak symplectic manifolds 3. Right invariant weak Riemannian metrics on Lie groups 4. The Hamiltonian approach 5. Vanishing geodesic distance on groups of diffeomorphisms 6. The regular Lie group of rapidly decreasing diffeomorphisms 7. The diffeomorphism group of S or R, and Burgers’ hierarchy 8. The Virasoro-Bott group and the Kort...

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the ...

A fast community detection algorithm based on a q-state Potts model is presented. Communities (groups of densely interconnected nodes that are only loosely connected to the rest of the network) are found to coincide with the domains of equal spin value in the minima of a modified Potts spin glass Hamiltonian. Comparing global and local minima of the Hamiltonian allows for the detection of overl...

Let (M,ω) be a connected symplectic manifold on which a connected Lie group G acts properly and in a Hamiltonian fashion with moment map μ : M −→ g∗. Our purpose is investigate multiplicity-free actions, giving criteria to decide a multiplicity freenes of the action. As an application we give the complete classification of multiplicity-free actions of compact Lie groups acting isometrically and...

This paper uses the machinery of symplectic geometry to make rigorous the mathematical framework of Hamiltonian mechanics. This framework is then shown to imply Newton’s laws and conservation of energy, thus validating it as a physical theory. We look at symmetries of physical systems in the form of Lie groups, and show that the Hamiltonian framework grants us the insight that the existence of ...