lemma 106.1 The short-time kernel

open in the book · parts/11-qft-standard-model/08-path-integral-quantization.tex:141 · p. 2156

Rests on

depends_on corollary 8.15 Deformation of contours ¶
- depends_on definition 6.17 Simply connected space ¶
  - depends_on definition 6.6 Continuous map ¶
    - depends_on definition 3.53 Preimage ¶
    - depends_on definition 6.2 Open set ¶
      - depends_on definition 6.1 Topological space ¶
    - depends_on definition 6.1 Topological space ¶ ↺
  - depends_on definition 6.15 Path-connected space ¶
    - depends_on definition 6.6 Continuous map ¶ ↺
- 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 6.9 Compact set ¶
    - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on definition 7.125 Multiple integral ¶
      - depends_on theorem 7.40 Continuous functions are integrable ¶
      - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
    - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - depends_on definition 7.41 Antiderivative ¶
      - depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
      - proves proof ch:05-real-analysis@proof-25 ¶
    - proves proof ch:05-real-analysis@proof-77 ¶
  - proves proof ch:06-complex-analysis@proof-7 ¶
- proves proof ch:06-complex-analysis@proof-9 ¶
depends_on lemma 106.2 Gaussian integrals ¶
- depends_on equation 17.42 eq:ft-gaussian ¶
- depends_on lemma 8.9 ML estimate ¶
  - depends_on equation 8.6 eq:cpx-contour-integral ¶
  - proves proof ch:06-complex-analysis@proof-4 ¶
- proves proof ch:08-path-integral-quantization@proof-2 ¶
proves proof ch:08-path-integral-quantization@proof-1 ¶

Supports

depends_on theorem 106.3 Feynman's sum over histories ¶
- depends_on phenomenon 106.5 The Aharonov–Bohm effect ¶
- depends_on theorem 106.16 Feynman–Kac ¶
  - depends_on proposition 106.17 Euclidean time projects onto the ground state ¶
    - depends_on phenomenon 106.77 The light hadron spectrum is a prediction of QCD ¶
    - depends_on proposition 106.71 The Wilson loop measures the static potential ¶
      - depends_on phenomenon 102.62 The static potential rises linearly ¶
  - depends_on proposition 106.21 Reflection positivity is the positivity of the Hilbert space ¶
    - depends_on proposition 109.82 Wilson's action is reflection positive ¶

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`	→	Deformation of contours	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:156
`depends_on`	→	Gaussian integrals	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:156
`depends_on`	←	Feynman's sum over histories	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:320
`proves`	←	ch:08-path-integral-quantization@proof-1	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:159