theorem 106.3 Feynman's sum over histories

open in the book · parts/11-qft-standard-model/08-path-integral-quantization.tex:297 · p. 2158

Rests on

depends_on equation 106.1 eq:pathint-propagator-def ¶
depends_on lemma 106.1 The short-time kernel ¶
- 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 6.15 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 remark 7.128 What the derivations below take as given ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - 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 ¶
proves proof ch:08-path-integral-quantization@proof-3 ¶

Supports

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`	→	eq:pathint-propagator-def	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:320
`depends_on`	→	The short-time kernel	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:320
`depends_on`	←	The Aharonov–Bohm effect	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:481
`depends_on`	←	Feynman–Kac	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:959
`proves`	←	ch:08-path-integral-quantization@proof-3	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:323