proposition 13.93 Algebra of densities

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:4557 · p. 509

Rests on

depends_on definition 13.92 Tensor density ¶
- depends_on definition 13.89 Contravariant and covariant tensors ¶
  - depends_on definition 13.88 General coordinate transformation ¶
- depends_on definition 13.88 General coordinate transformation ¶ ↺
proves proof ch:11-manifolds-tensors-curvature@proof-17 ¶

Supports

depends_on example 13.94 The two densities this chapter uses ¶
- depends_on lemma 14.62 The Levi-Civita symbol is invariant ¶
  - depends_on definition 29.4 Angular velocity ¶
    - depends_on proposition 29.11 Angular velocity in Euler angles ¶
      - depends_on definition 29.35 The Lagrange top ¶
      - depends_on remark 29.12 The coordinate singularity, and what it is not ¶
    - depends_on proposition 29.5 The velocity field of a rigid body ¶
      - depends_on proposition 29.14 Angular momentum and kinetic energy ¶
      - depends_on proposition 29.8 Chasles: the general displacement is a screw ¶
      - depends_on proposition 29.6 The angular velocity does not depend on the base point ¶
      - depends_on theorem 29.7 Transport theorem ¶
    - depends_on theorem 29.7 Transport theorem ¶ ↺
  - depends_on lemma 14.64 Properties of $W$ ¶
    - depends_on theorem 14.65 The two Casimir operators of the Poincaré algebra in $3+1$ dimensions ¶
      - depends_on example A.394 $D = 4$ ¶

Neighborhood

Every logical edge within two steps of this node.

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Edges

type	direction	node	provenance	where
`depends_on`	→	Tensor density	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:4563
`depends_on`	←	The two densities this chapter uses	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:4597
`proves`	←	ch:11-manifolds-tensors-curvature@proof-17	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:4566