proposition 99.25 The one-quantum sector is an irreducible representation
open in the book ·
parts/11-qft-standard-model/01-canonical-quantization.tex:1709
· p. 1874
Rests on
- depends_on definition 94.15 Pauli–Lubanski vector ¶
-
depends_on
proposition 99.24
Translations act correctly on the field
¶
- depends_on equation 99.31 eq:canq-ladder ¶
- depends_on equation 99.34 eq:canq-momentum-modes ¶
-
depends_on
proposition 99.6
The Heisenberg equations reproduce the field
equation
¶
- depends_on equation 99.23 eq:canq-ccr ¶
- depends_on equation 99.24 eq:canq-ccr-zero ¶
- depends_on equation 99.21 eq:canq-scalar-hamiltonian ¶
- proves proof ch:01-canonical-quantization@proof-2 ¶
- proves proof ch:01-canonical-quantization@proof-12 ¶
-
depends_on
theorem 94.18
The Casimir invariants of the Poincaré group
¶
- proves derived proof ch:03-poincare-representations@proof-11 ¶
- proves proof ch:01-canonical-quantization@proof-13 ¶
Supports
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Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Pauli–Lubanski vector | declared | parts/11-qft-standard-model/01-canonical-quantization.tex:1723 |
depends_on |
→ | Translations act correctly on the field | declared | parts/11-qft-standard-model/01-canonical-quantization.tex:1723 |
depends_on |
→ | The Casimir invariants of the Poincaré group | declared | parts/11-qft-standard-model/01-canonical-quantization.tex:1723 |
proves |
← | ch:01-canonical-quantization@proof-13 | declared | parts/11-qft-standard-model/01-canonical-quantization.tex:1727 |