Overview of symbols and notations used throughout these pages
The tables on this page provide an overview of the main symbols and notations used throughout this documentation. We also mention differences to other common conventions in the literature.
Basic objects ¶ Object Symbol used here Other commonly used symbols Bare propagator G 0 G_0 G 0 G 0 G^{0} G 0 Dressed propagator G G G g g g Bubble (i.e. propgator pair) χ 0 \chi_0 χ 0 χ 0 \chi^{0} χ 0 Π \Pi Π ( G G ) (GG) ( GG ) Self-energy Σ \Sigma Σ - Bare four-point vertex F 0 F_0 F 0 U U U V V V Γ 0 \Gamma_{0} Γ 0 Γ 0 \Gamma^{0} Γ 0 f f f Full four-point vertex F F F Γ \Gamma Γ Γ ( 4 ) \Gamma^{(4)} Γ ( 4 ) Γ ∗ \Gamma^* Γ ∗ f f f V V V L X L^X L X Four-point Green’s function G ( 4 ) G^{(4)} G ( 4 ) g ( 4 ) g^{(4)} g ( 4 ) G 2 G_2 G 2
Parquet theory ¶ Object Symbol used here Other commonly used symbols two-particle channels p h ‾ \overline{ph} p h p p pp pp p h ph p h (a a a p p p t t t x x x p p p d d d u u u s s s t t t two-particle reducible vertex in channel r r r Φ r \Phi^r Φ r γ r \gamma_r γ r ϕ r \phi_r ϕ r Φ r \Phi_r Φ r two-particle irreducible vertex in channel r r r Γ r \Gamma^r Γ r I r I_r I r Γ r \Gamma_r Γ r fully irreducible vertex Λ \Lambda Λ R R R Λ ~ \tilde{\Lambda} Λ ~ I \mathcal{I} I Λ 2 P I \Lambda_{2\mathrm{PI}} Λ 2 PI
Single boson exchange (SBE) theory ¶ Object Symbol used here Other commonly used symbols U U U r r r Δ r \Delta^r Δ r ∇ r \nabla_r ∇ r M \mathcal{M} M C \mathcal{C} C S \mathcal{S} S U U U r r r T r T^r T r ϕ r \phi^r ϕ r I r \mathcal{I}^r I r fully U U U Λ U \Lambda^{U} Λ U ϕ U i r r \phi^{U_\mathrm{irr}} ϕ U irr ϕ f i r r \phi^\mathrm{firr} ϕ firr Λ U i r r \Lambda^{\mathrm{Uirr}} Λ Uirr Λ U i r r \Lambda_{U \mathrm{irr}} Λ U irr I U i r r \mathcal{I}_{U \mathrm{irr}} I U irr Φ U i r r \Phi^\mathrm{Uirr} Φ Uirr screened interaction in channel r r r W r W^r W r w r w_r w r η r \eta_r η r W r W_r W r D r D^r D r Hedin vertices in channel r r r (γ r \gamma^r γ r γ ‾ r \overline{\gamma}^r γ r (λ r \lambda_r λ r λ ˉ r \bar{\lambda}_r λ ˉ r Λ r \Lambda_r Λ r Λ ˉ r \bar{\Lambda}_r Λ ˉ r h r h^r h r h ˉ r \bar{h}^r h ˉ r polarization in channel r r r P r P^r P r Π r \Pi_r Π r π r \pi_r π r P r P_r P r
Frequency and momentum parametrizations ¶ Object Symbol used here Other commonly used symbols bosonic frequency ω \omega ω Ω \Omega Ω ω ˉ \bar{\omega} ω ˉ ν ˉ \bar{\nu} ν ˉ fermionic frequency ν \nu ν ω \omega ω bosonic momentum q \mathbf{q} q Q \mathbf{Q} Q fermionic momentum k \mathbf{k} k -
Object Symbol used here Other commonly used symbols contour indices c i ∈ { − , + } c_i \in \{-, +\} c i ∈ { − , + } j i j_i j i Keldysh indices k i ∈ { 1 , 2 } k_i \in \{1,2\} k i ∈ { 1 , 2 } α i \alpha_i α i κ i \kappa_i κ i