theorem 115.31 Second-order Fermi acceleration

open in the book · parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2140 · p. 2515

Rests on

depends_on definition 40.1 Four-vector ¶
- 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 ¶
      - depends_on notation 38.3 Standard configuration ¶
      - depends_on postulate 38.2 Invariance of the speed of light ¶
      - depends_on postulate 38.1 Principle of relativity ¶
      - proves proof ch:02-lorentz-transformations@proof-1 ¶
    - proves proof ch:02-lorentz-transformations@proof-2 ¶
- depends_on equation 38.14 eq:lor-invariance-condition ¶
depends_on equation 40.3 eq:rdyn-fourmomentum ¶
proves proof ch:17-cosmic-rays-astroparticle@proof-24 ¶

Supports

depends_on theorem 115.33 The spectrum from a strong shock ¶

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-vector	declared	parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2151
`depends_on`	→	eq:rdyn-fourmomentum	declared	parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2151
`depends_on`	←	The spectrum from a strong shock	declared	parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2255
`proves`	←	ch:17-cosmic-rays-astroparticle@proof-24	declared	parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2154