User:Waterbug89/Books/Hamiltonian Mechanics and Mathematics

Hamiltonian Mechanics and Mathematics

 * Basic Concepts
 * Classical mechanics
 * Dynamical system
 * Equations of motion
 * Canonical transformations
 * Generalized coordinates
 * Phase space


 * Hamiltonian mechanics
 * William Rowan Hamilton
 * Hamilton's principle
 * Hamiltonian mechanics
 * Hamiltonian vector field
 * Hamilton–Jacobi equations
 * Lie bracket of vector fields
 * Euler–Lagrange equations
 * Lagrangian mechanics
 * Legendre transformations
 * Legendre–Fenchel transformations
 * Poisson bracket
 * Poisson algebra
 * Poisson manifold
 * Vector space


 * Differential Geometry and Molecular Mechanics
 * Differential geometry
 * Symplectic vector space
 * Symplectic manifold
 * Symplectic group
 * Almost complex manifold
 * Symplectic matrix
 * Symplectic representation
 * Symplectic sum
 * Symplectic geometry
 * Symplectomorphisms
 * Algebraic geometry
 * Category theory


 * Molecular Dynamics and Integrators
 * Dynamical system
 * Symplectic integrator
 * Molecular dynamics
 * Molecular modelling


 * Relativity Theory
 * Einstein–Hilbert action
 * General relativity
 * Einstein field equations
 * Solutions of the Einstein field equations
 * Spherical coordinate system
 * Maxwell's equations in curved spacetime
 * Riemannian manifolds
 * Pseudo-Riemannian manifolds


 * Quantum Theory in Feynman's Formulation and Hamiltonian formalism inadequacies
 * Quantum mechanics
 * Commutators
 * Canonical quantization
 * Moyal bracket
 * Path integral formulation
 * Dirac bracket
 * Quantum field theory
 * Jacobi identity
 * Lie algebra
 * Lie groups
 * Lie theory
 * Lie groupoids
 * Lie algebroids
 * R-algebroid
 * Algebraic topology
 * Double groupoids
 * Higher-dimensional algebra
 * Poisson superalgebra


 * Quantum Symmetry and TQFT
 * Symmetry
 * Chiral symmetry
 * Loop quantum cosmology
 * Quantum cohomology
 * Topological quantum field theory
 * Standard Model
 * Quantum anomalies
 * Supersymmetry (SUSY)
 * Minimal Supersymmetric Standard Model (MSSM)


 * Statistical Physics and Quantum Theory
 * Exchange symmetry
 * Statistical physics
 * Statistical mechanics
 * Statistical field theory
 * Ergodic theory