theorem 38.23 Polar decomposition of a Lorentz transformation
open in the book ·
parts/04-special-relativity/02-lorentz-transformations.tex:848
· p. 1218
Rests on
-
depends_on
definition 39.5
Orthochronous Lorentz group
¶
-
depends_on
definition 39.1
Lorentz group
¶
-
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 38.6
Minkowski metric and interval
¶
-
depends_on
equation 39.3
eq:mink-noncompact
¶
- step_from equation 39.2 eq:mink-lorentz-condition ¶
-
depends_on
definition 39.1
Lorentz group
¶
- depends_on equation 38.20 eq:lor-genboost-00 ¶
- depends_on equation 38.22 eq:lor-genboost-i0 ¶
- depends_on equation 38.14 eq:lor-invariance-condition ¶
-
depends_on
proposition 39.6
$L^{\uparrow}$ and $L^{\uparrow}_{+}$ are
subgroups
¶
- depends_on definition 39.5 Orthochronous Lorentz group ¶ ↺
- depends_on equation 39.2 eq:mink-lorentz-condition ¶ ↺
- depends_on equation 39.3 eq:mink-noncompact ¶ ↺
- proves proof ch:03-minkowski-lorentz-poincare@proof-3 ¶
- proves proof ch:02-lorentz-transformations@proof-10 ¶
Supports
- depends_on remark 38.24 Boosts alone do not form a 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 |
→ | Orthochronous Lorentz group | declared | parts/04-special-relativity/02-lorentz-transformations.tex:856 |
depends_on |
→ | eq:lor-genboost-00 | declared | parts/04-special-relativity/02-lorentz-transformations.tex:856 |
depends_on |
→ | eq:lor-genboost-i0 | declared | parts/04-special-relativity/02-lorentz-transformations.tex:856 |
depends_on |
→ | eq:lor-invariance-condition | declared | parts/04-special-relativity/02-lorentz-transformations.tex:856 |
depends_on |
→ | $L^{\uparrow}$ and $L^{\uparrow}_{+}$ are subgroups | declared | parts/04-special-relativity/02-lorentz-transformations.tex:856 |
depends_on |
← | Boosts alone do not form a group | declared | parts/04-special-relativity/02-lorentz-transformations.tex:915 |
proves |
← | ch:02-lorentz-transformations@proof-10 | declared | parts/04-special-relativity/02-lorentz-transformations.tex:859 |