definition 40.4 Four-momentum

open in the book · parts/04-special-relativity/04-relativistic-dynamics.tex:77 · p. 1230

ground object -- no derivation owed

Rests on

depends_on definition 40.2 Four-velocity ¶
- depends_on definition 38.12 Proper time ¶
  - depends_on definition 38.6 Minkowski metric and interval ¶
    - depends_on proposition 38.5 The invariant interval ¶
      - depends_on equation 38.1 eq:lor-beta-gamma ¶
      - depends_on theorem 38.4 Lorentz boost ¶
      - proves proof ch:02-lorentz-transformations@proof-2 ¶
  - depends_on proposition 38.5 The invariant interval ¶ ↺
- depends_on definition 40.1 Four-vector ¶
  - depends_on definition 38.6 Minkowski metric and interval ¶ ↺
  - depends_on equation 38.14 eq:lor-invariance-condition ¶

Supports

depends_on definition 40.9 Four-force ¶
depends_on definition 40.12 Invariant mass ¶
- depends_on example 40.13 Threshold energy for pair production ¶
depends_on phenomenon 99.3 Electron–positron pair creation ¶
depends_on postulate 40.11 Conservation of four-momentum ¶
- depends_on example 40.14 Compton scattering ¶
- depends_on example 40.13 Threshold energy for pair production ¶ ↺
depends_on theorem 40.5 Energy–momentum relation ¶
- depends_on example 40.14 Compton scattering ¶ ↺
- depends_on phenomenon 99.3 Electron–positron pair creation ¶ ↺
- depends_on proposition 26.29 Reparametrization invariance and the mass-shell constraint ¶
- depends_on proposition 49.2 Ground-state pressure of the ideal Fermi gas ¶
  - depends_on phenomenon 49.6 A maximum mass for a cold degenerate star ¶
  - depends_on phenomenon 49.8 The white-dwarf luminosity function has an edge ¶
  - depends_on phenomenon 49.1 Matter at a billion kilograms per cubic metre ¶
  - depends_on theorem 49.7 The Chandrasekhar mass ¶
    - depends_on phenomenon 49.6 A maximum mass for a cold degenerate star ¶ ↺

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`	→	Four-velocity	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:90
`depends_on`	←	Four-force	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:180
`depends_on`	←	Invariant mass	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:266
`depends_on`	←	Electron–positron pair creation	declared	parts/11-qft-standard-model/01-canonical-quantization.tex:222
`depends_on`	←	Conservation of four-momentum	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:249
`depends_on`	←	Energy–momentum relation	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:98