lemma 106.2 Gaussian integrals

open in the book · parts/11-qft-standard-model/08-path-integral-quantization.tex:225 · p. 2157

Rests on

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 ¶

Supports

depends_on lemma 106.1 The short-time kernel ¶
- 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 proposition 106.21 Reflection positivity is the positivity of the Hilbert space ¶
      - depends_on proposition 109.82 Wilson's action is reflection positive ¶
depends_on theorem 106.27 The free generating functional and the Feynman propagator ¶
depends_on theorem 106.54 The gauge-fixed action ¶
- depends_on proposition 106.55 Ghosts are required by unitarity ¶

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:ft-gaussian	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:245
`depends_on`	→	ML estimate	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:245
`depends_on`	←	The short-time kernel	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:156
`depends_on`	←	The free generating functional and the Feynman propagator	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:1475
`depends_on`	←	The gauge-fixed action	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:2651
`proves`	←	ch:08-path-integral-quantization@proof-2	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:248