---
artifact_kind: l1_convention_snapshot
notation_choices: 'Hedin 1965: G=Green function, W=screened Coulomb, Sigma=self-energy,
  Gamma=vertex, P=polarizability'
stage: L1
unit_conventions: Atomic units (Hartree/Bohr). eV for band gap reporting.
---
# Convention Snapshot

## Notation Choices
Hedin 1965 conventions as canonical:
- G(1,2): single-particle Green function
- W(1,2): dynamically screened Coulomb interaction
- Sigma(1,2): electron self-energy Sigma = iGW
- Gamma(1,2;3): irreducible vertex function

## Unit Conventions
Atomic units. eV for reporting.

## Sign Conventions
- Time-ordered Greens functions
- Self-energy: Sigma = iGW (Hedin convention)
- Fourier: int domega/(2pi)

## Metric Or Coordinate Conventions
Real space, plane-wave basis.

## Categorized Assumptions
### Mathematical assumptions
Translational invariance, single Slater determinant reference.
### Physical assumptions
T=0, no SOC, weak-to-moderate correlation.
### Notational assumptions
Spin sum implicit, 1+ = t1+eta.

## Canonical Notation
Hedin 1965 canonical. All GW literature derives from it.

## Unresolved Tensions
Time-ordered vs retarded G for spectral properties.

## L3 Discoveries
(To be appended during derivation)

