Physics / advanced
Generating functionals and quantum correlations
Build path-integral methods from time slicing to functional derivatives, effective actions, and carefully defined Euclidean continuation.
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Inside this module
Module 01 advanced
Generating functionals and quantum correlations
Build path-integral methods from time slicing to functional derivatives, effective actions, and carefully defined Euclidean continuation.
- 01
Build a path integral from short evolution steps
Keep endpoints, short-time normalization, and the limiting procedure explicit.
27 min - 02
Reduce a regulated Gaussian to its eigenmodes
Separate normalization determinants, covariances, zero modes, and boundary conditions.
27 min - 03
Generate moments with a declared source convention
Derive source differentiation on a finite regulator before using functional notation.
27 min - 04
Extract connected fluctuations with a logarithm
Distinguish full moments, cumulants, vacuum normalization, and Gaussian pairing.
27 min - 05
Trade the source for the mean field
State convexity and inverse-response assumptions before identifying irreducible vertices.
27 min - 06
Fix ordering before integrating fermionic variables
Define a finite Berezin algebra and derive its determinant rather than treating it as a probability integral.
27 min - 07
Continue evolution while preserving its analytic meaning
Track the time contour, the action sign, spectral damping, and reconstruction assumptions.
27 min - 08
Derive quantum equations with their contact terms
Use finite integration by parts to separate exact identities from closure assumptions.
27 min - 09
Expand around a background without forgetting constraints
Use regulated Hessians, determinant ratios, and gauge-orbit Jacobians consistently.
27 min - 10
Extract scattering from physical external poles
Specify state normalization, residues, amputation, and the scope of asymptotic particles.
27 min