proposition 23.44 Relativistic Hamilton–Jacobi equation

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:1447 · p. 840

Rests on

depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
- depends_on definition 13.48 Differentiable manifold ¶
  - depends_on definition 13.47 Differentiable structure ¶
    - depends_on definition 13.44 Atlas ¶
      - depends_on definition 13.43 Coordinate system ¶
- depends_on definition 13.84 Tensor ¶
  - depends_on definition 13.83 Covector ¶
    - depends_on definition 13.81 Vector on a manifold ¶
      - depends_on definition 13.71 Differentiable curve ¶
      - depends_on definition 13.45 Differentiable map on a topological space ¶
      - depends_on definition 13.48 Differentiable manifold ¶ ↺
  - depends_on definition 13.81 Vector on a manifold ¶ ↺
depends_on equation 23.2 eq:hj-equation ¶
depends_on equation 40.5 eq:rdyn-dispersion ¶
proves proof ch:06-hamilton-jacobi@proof-13 ¶

Supports

depends_on remark 23.46 Carter's constant ¶
depends_on remark 23.45 Why this is not an analogy ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Metric tensor of signature $(p,q)$	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1469
`depends_on`	→	eq:hj-equation	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1469
`depends_on`	→	eq:rdyn-dispersion	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1469
`depends_on`	←	Carter's constant	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1548
`depends_on`	←	Why this is not an analogy	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1516
`proves`	←	ch:06-hamilton-jacobi@proof-13	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1472