equation 39.3 eq:mink-noncompact

open in the book · parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:133

connected by a declared semantic edge

Rests on

step_from equation 39.2 eq:mink-lorentz-condition ¶

Supports

depends_on definition 39.7 Antichronous transformations ¶
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 proposition 39.6 $L^{\uparrow}$ and $L^{\uparrow}_{+}$ are subgroups ¶ ↺

Neighborhood

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Edges

type	direction	node	provenance	where
`step_from`	→	eq:mink-lorentz-condition	declared — the $\mu=\nu=0$ component of the defining relation	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:136
`depends_on`	←	Antichronous transformations	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:284
`depends_on`	←	Orthochronous Lorentz group	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:223
`depends_on`	←	$L^{\uparrow}$ and $L^{\uparrow}_{+}$ are subgroups	declared	parts/04-special-relativity/03-minkowski-lorentz-poincare.tex:233