nLab symplectic geometry - contents

symplectic geometry

higher symplectic geometry

Background

• geometry

• differential geometry

Basic concepts

• almost symplectic structure, metaplectic structure, metalinear structure

• symplectic form, n-plectic form

• symplectic Lie n-algebroid

  • symplectic manifold

  • Poisson manifold, Poisson Lie algebroid

    Poisson n-algebra

  • Courant Lie 2-algebroid

• symplectic infinity-groupoid

  • symplectic groupoid

• symplectomorphism, symplectomorphism group

  • symplectic vector field, Hamiltonian vector field

    • Hamiltonian, Hamiltonian form

  • symplectic gradient

• Hamiltonian action, moment map

• symplectic reduction, BRST-BV formalism

• isotropic submanifold, Lagrangian submanifold, polarization

Classical mechanics and quantization

• Hamiltonian mechanics

• quantization

  deformation quantization,

  geometric quantization, higher geometric quantization

  • geometric quantization of symplectic groupoids

  • prequantum line bundle, prequantum circle n-bundle

    • contact manifold, contactomorphism

    • contact form, Reeb vector field

  • quantomorphism group, quantomorphism n-group

    • Poisson bracket, Poisson algebra

    • Poisson bracket Lie n-algebra

    • Heisenberg Lie algebra, Heisenberg Lie n-algebra

    • Heisenberg group

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