Book “Hamiltonian Mechanics, Quantum Theory, Relativity and Geometry Vol.2”

US$ 38.70*

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

Book size: ca. 696 pages






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