Book “Hamiltonian Mechanics, Quantum Theory, Relativity and Geometry Vol.2”
Title:
Hamiltonian Mechanics, Quantum Theory, Relativity and Geometry Vol.2
Subtitle:
Symplectic Geometry, TQFT, Algebraic Topology and Algebraic Geometry
Editor:
By Wikipedians
Language:
English
Wiki page:
Book:Hamiltonian Mechanics and Mathematics
Categories:
Mathematics
Contents:
- Chapter: Basic Concepts
- Classical mechanics
- Dynamical system
- Equations of motion
- Canonical transformations
- Generalized coordinates
- Phase space
- Chapter: 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
- Chapter: 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
- Chapter: Molecular Dynamics and Integrators
- Dynamical system
- Symplectic integrator
- Molecular dynamics
- Molecular modelling
- Chapter: 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
- Chapter: 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
- Chapter: 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)
- Chapter: Statistical Physics and Quantum Theory
- Exchange symmetry
- Statistical physics
- Statistical mechanics
- Statistical field theory
- Ergodic theory