proposition 25.14 The Galilei cocycle is not a coboundary
open in the book ·
parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:594
· p. 879
Rests on
- depends_on definition 14.72 Central extension ¶
- depends_on equation 25.15 eq:pq-galilei-central ¶
-
depends_on
proposition 14.73
The extension datum is a $2$-cocycle
¶
- depends_on definition 14.72 Central extension ¶ ↺
- proves proof ch:12-lie-groups-fibre-bundles@proof-35 ¶
- proves proof ch:08-poisson-quantum-bridge@proof-7 ¶
Supports
-
depends_on
corollary 15.36
Bargmann in $3{+}1$, extended Bargmann in $2{+}1$
¶
- depends_on example 15.64 The whole chapter at $D=4$ ¶
- depends_on remark 15.59 The central charge is what makes the form work ¶
- depends_on example 14.80 The Galilei algebra ¶
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 |
→ | Central extension | declared | parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:608 |
depends_on |
→ | eq:pq-galilei-central | declared | parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:608 |
depends_on |
→ | The extension datum is a $2$-cocycle | declared | parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:608 |
depends_on |
← | Bargmann in $3{+}1$, extended Bargmann in $2{+}1$ | declared | parts/02-mathematical-methods/13-lie-algebra-expansions.tex:1284 |
depends_on |
← | The Galilei algebra | declared | parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:3549 |
proves |
← | ch:08-poisson-quantum-bridge@proof-7 | declared | parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:611 |