definition 39.1 Lorentz group

open in the book · parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:59 · p. 1221

ground object -- no derivation owed

Rests on

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 ¶

Supports

depends_on definition 39.4 Improper Lorentz transformations ¶
- depends_on proposition 39.8 Component structure ¶
depends_on definition 39.5 Orthochronous Lorentz group ¶
- depends_on definition 39.7 Antichronous transformations ¶
- depends_on lemma 109.42 Total inversion is a complex Lorentz transformation ¶
  - depends_on corollary 109.43 Total inversion is automatic ¶
    - depends_on theorem 109.44 Jost ¶
      - depends_on corollary 109.45 Locality implies $PCT$ ¶
    - depends_on theorem 109.49 Spin and statistics ¶
      - depends_on corollary 109.50 The connection between spin and statistics ¶
- depends_on proposition 39.8 Component structure ¶ ↺
- depends_on proposition 39.6 $L^{\uparrow}$ and $L^{\uparrow}_{+}$ are subgroups ¶
  - depends_on theorem 38.23 Polar decomposition of a Lorentz transformation ¶
    - depends_on remark 38.24 Boosts alone do not form a group ¶
- depends_on theorem 105.34 $CPT$ ¶
  - assumes experiment CP Violation ¶
    - cites (data) derived bib 22 First Observation ofCPViolation in the Decays ofBs0Mesons ¶
    - cites (data) derived bib 22 First Observation ofCPViolation in the Decays ofBs0Mesons ¶ ↺
    - cites (evidence) derived bib 22 First Observation ofCPViolation in the Decays ofBs0Mesons ¶ ↺
    - cites (evidence) derived bib 22 First Observation ofCPViolation in the Decays ofBs0Mesons ¶ ↺
    - cites (evidence) derived bib 21 Observation of CP Violation in Charm Decays ¶
    - cites (data) derived bib 21 Observation of CP Violation in Charm Decays ¶ ↺
    - cites (evidence) derived bib 21 Observation of CP Violation in Charm Decays ¶ ↺
    - cites (evidence) derived bib 9 Observation of LargeCPViolation in the NeutralBMeson System ¶
    - cites (data) derived bib 9 Observation of LargeCPViolation in the NeutralBMeson System ¶ ↺
    - cites (data) derived bib 9 Observation of LargeCPViolation in the NeutralBMeson System ¶ ↺
    - cites (evidence) derived bib 9 Observation of LargeCPViolation in the NeutralBMeson System ¶ ↺
    - cites (data) derived bib 8 Measurement of the Permanent Electric Dipole Moment of the Neutron ¶
    - … 109 more
  - depends_on phenomenon 111.9 Charge asymmetry in semileptonic kaon decay ¶
  - depends_on proposition 105.40 Greenberg ¶
  - depends_on theorem 105.38 Equal total lifetimes ¶
    - assumes experiment CP Violation ¶ ↺
    - depends_on proposition 105.39 A direct $CP$ asymmetry needs two amplitudes and two kinds of phase ¶
      - depends_on phenomenon 111.15 CP violation in charm decay ¶
      - depends_on phenomenon 111.11 Direct CP violation in kaon decay ¶
  - depends_on theorem 105.36 Equal masses ¶
    - assumes experiment CP Violation ¶ ↺
    - depends_on phenomenon 111.17 The universe is made of matter ¶
  - depends_on theorem 105.41 Sakharov's conditions ¶
    - depends_on phenomenon 111.17 The universe is made of matter ¶ ↺
    - depends_on phenomenon 103.44 The universe contains matter and almost no antimatter ¶
- depends_on theorem 38.23 Polar decomposition of a Lorentz transformation ¶ ↺
depends_on definition 39.10 Poincaré group ¶
- depends_on proposition 39.11 Invariance of the interval ¶
depends_on definition 39.3 Proper Lorentz group ¶
depends_on proposition 39.9 The generators ¶
depends_on proposition 39.2 $L$ is a Lie group ¶

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`	→	Minkowski metric and interval	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:65
`depends_on`	←	Improper Lorentz transformations	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:184
`depends_on`	←	Orthochronous Lorentz group	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:223
`depends_on`	←	Poincaré group	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:486
`depends_on`	←	Proper Lorentz group	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:169
`depends_on`	←	The generators	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:366
`depends_on`	←	$L$ is a Lie group	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:75