gravity, supergravity

Formalism

• Poincare Lie algebra

  • super Poincare Lie algebra, supergravity Lie 3-algebra, supergravity Lie 6-algebra

• differential geometry

  • pseudo-Riemannian manifold

  • spacetime, smooth Lorentzian manifold

Definition

• Einstein-Hilbert action, Einstein's equations, general relativity

  • first-order formulation of gravity, D'Auria-Fre formulation of supergravity

  • gravity as a BF-theory, Plebanski formulation of gravity, teleparallel gravity

Spacetime configurations

• spacetime

• Minkowski spacetime

• black hole spacetime

  • Schwarzschild spacetime

  • Kerr spacetime

Properties

• Bekenstein-Hawking entropy

• generalized second law of thermodynamics

Models

• standard model of cosmology

• 11-dimensional supergravity

• Kaluza-Klein mechanism

Quantum theory

• quantum gravity

  • graviton, gravitino

  • string theory

physics, mathematical physics

Surveys, textbooks and lecture notes

• (higher) category theory and physics

• geometry of physics

• books and reviews, physics resources

theory (physics), model (physics)

• mechanics

  • mass, charge, momentum, angular momentum, moment of inertia

  • dynamics on Lie groups

    • rigid body dynamics

• field (physics)

  • Lagrangian mechanics

    • configuration space, state

    • action functional, Lagrangian

    • covariant phase space, Euler-Lagrange equations

  • Hamiltonian mechanics

    • phase space

    • symplectic geometry

      • Poisson manifold

      • symplectic manifold

      • symplectic groupoid

    • multisymplectic geometry

      • n-symplectic manifold

  • spacetime

    • smooth Lorentzian manifold

    • special relativity

    • general relativity

    • gravity

      • supergravity, dilaton gravity

      • black hole

• Classical field theory

  • classical physics

    • classical mechanics
    • waves and optics
    • thermodynamics

• Quantum Mechanics

  • in terms of †-compact categories

  • quantum information

  • Hamiltonian operator

  • density matrix

  • Kochen-Specker theorem

  • Bell's theorem

  • Gleason's theorem

• Quantization

  • geometric quantization

  • deformation quantization

  • path integral quantization

  • semiclassical approximation

• Quantum Field Theory

  • Axiomatizations

    • algebraic QFT

      • Wightman axioms

      • Haag-Kastler axioms

        • operator algebra

        • local net

          • conformal net

      • Reeh-Schlieder theorem

      • Osterwalder-Schrader theorem

      • PCT theorem

      • Bisognano-Wichmann theorem

        • modular theory

      • spin-statistics theorem

        • boson, fermion

    • functorial QFT

      • cobordism

      • (∞,n)-category of cobordisms

      • cobordism hypothesis-theorem

      • extended topological quantum field theory

  • Tools

    • perturbative quantum field theory, vacuum

    • effective quantum field theory

    • renormalization

    • BV-BRST formalism

    • geometric ∞-function theory

  • particle physics

    • phenomenology

    • models

      • standard model of particle physics

      • fields and quanta

      • Grand Unified Theories, MSSM

    • scattering amplitude

      • on-shell recursion, KLT relations

  • Structural phenomena

    • universality class

    • quantum anomaly

      • Green-Schwarz mechanism

    • instanton

    • spontaneously broken symmetry

    • Kaluza-Klein mechanism

    • integrable systems

    • holonomic quantum fields

  • Types of quantum field thories

    • TQFT

      • 2d TQFT

      • Dijkgraaf-Witten theory

      • Chern-Simons theory

    • TCFT

      • A-model, B-model

      • homological mirror symmetry

    • QFT with defects

    • conformal field theory

    • (1,1)-dimensional Euclidean field theories and K-theory

    • (2,1)-dimensional Euclidean field theory and elliptic cohomology

    • CFT

      • WZW model

      • 6d (2,0)-supersymmetric QFT

    • gauge theory

      • field strength

      • gauge group, gauge transformation, gauge fixing

      • examples

        • electromagnetic field, QED

          • electric charge
          • magnetic charge

        • Yang-Mills field, QCD

          • Yang-Mills theory
          • spinors in Yang-Mills theory
          • topological Yang-Mills theory

        • Kalb-Ramond field

        • supergravity C-field

        • RR field

        • first-order formulation of gravity

          • general covariance
          • supergravity * D'Auria-Fre formulation of supergravity
          • gravity as a BF-theory

    • sigma-model

      • particle, relativistic particle, fundamental particle, spinning particle, superparticle

      • string, spinning string, superstring

      • membrane

      • AKSZ theory

• String Theory

  • string theory results applied elsewhere

superalgebra

and

supergeometry

Formal context

• superpoint

• super ∞-groupoid, smooth super ∞-groupoid, synthetic differential super ∞-groupoid

• synthetic differential supergeometry

Superalgebra

• super vector space, SVect

• super algebra

  • Grassmann algebra

  • Clifford algebra

• superdeterminant

• super Lie algebra

  • super Poincare Lie algebra

Supergeometry

• supermanifold, SDiff

  • super Lie group

    • super translation group

    • super Euclidean group

  • NQ-supermanifold

  • super vector bundle

  • complex supermanifold

  • Euclidean supermanifold

• integration over supermanifolds

  • Berezin integral

Structures

• supersymmetry

• division algebra and supersymmetry

Applications

• supergravity

• supersymmetric quantum mechanics

• geometric model for elliptic cohomology