proposition 106.14 The Feynman contour permits the rotation
open in the book ·
parts/11-qft-standard-model/08-path-integral-quantization.tex:855
· p. 2164
Rests on
- depends_on equation 100.23 eq:qed-fermion-propagator ¶
-
depends_on
lemma 8.9
ML estimate
¶
- depends_on equation 8.6 eq:cpx-contour-integral ¶
- proves proof ch:06-complex-analysis@proof-4 ¶
-
depends_on
theorem 8.12
Cauchy
¶
- depends_on equation 8.5 eq:cpx-cr ¶
-
depends_on
theorem 7.131
Green
¶
-
depends_on
definition 7.127
Simple regions
¶
-
depends_on
definition 7.98
Functions of class $C^{1}$
¶
- depends_on definition 7.20 Continuity at a point ¶
- depends_on definition 7.97 Partial derivative; gradient ¶
-
depends_on
definition 6.9
Compact set
¶
- depends_on definition 6.5 Open cover ¶
-
depends_on
definition 7.98
Functions of class $C^{1}$
¶
-
depends_on
remark 7.128
What the derivations below take as given
¶
-
depends_on
definition 7.125
Multiple integral
¶
- depends_on axiom 7.1 Completeness of $\R$ ¶
- depends_on definition 7.39 Darboux sums and the definite integral ¶
-
depends_on
theorem 7.40
Continuous functions are integrable
¶
- depends_on definition 7.39 Darboux sums and the definite integral ¶ ↺
- depends_on theorem 7.24 Extreme value theorem ¶
- depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
- proves proof ch:05-real-analysis@proof-23 ¶
- depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶ ↺
-
depends_on
definition 7.125
Multiple integral
¶
-
depends_on
theorem 7.43
Fundamental theorem of calculus, II
¶
-
depends_on
definition 7.41
Antiderivative
¶
- depends_on corollary 7.36 cor:ana-mvt-consequences ¶
- depends_on definition 7.26 Derivative of a function at a point ¶
-
depends_on
theorem 7.42
Fundamental theorem of calculus, I
¶
- depends_on definition 7.26 Derivative of a function at a point ¶ ↺
- depends_on theorem 7.40 Continuous functions are integrable ¶ ↺
- depends_on theorem 7.24 Extreme value theorem ¶ ↺
- proves proof ch:05-real-analysis@proof-24 ¶
- proves proof ch:05-real-analysis@proof-25 ¶
-
depends_on
definition 7.41
Antiderivative
¶
- proves proof ch:05-real-analysis@proof-77 ¶
-
depends_on
definition 7.127
Simple regions
¶
- proves proof ch:06-complex-analysis@proof-7 ¶
- proves proof ch:08-path-integral-quantization@proof-11 ¶
Supports
Nothing declares a dependency on this node yet.
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 |
→ | eq:qed-fermion-propagator | declared | parts/11-qft-standard-model/08-path-integral-quantization.tex:867 |
depends_on |
→ | ML estimate | declared | parts/11-qft-standard-model/08-path-integral-quantization.tex:867 |
depends_on |
→ | Cauchy | declared | parts/11-qft-standard-model/08-path-integral-quantization.tex:867 |
proves |
← | ch:08-path-integral-quantization@proof-11 | declared | parts/11-qft-standard-model/08-path-integral-quantization.tex:870 |