Module coupling 

Degree terms (p, weight) of the spherical translation coefficients, from the Wigner 3j couplings of a source and a destination mode.

Upstream: treams.special._tl_vsw_helper and the degree sums of tl_vsw_A and tl_vsw_B.

Structs

Coupling 🔒

The degree terms (p, weight) coupling a source (l, m) to a destination (lambda, mu), for all four polarization pairs. The parity basis couples equal polarizations through same and opposite ones through cross; the helicity basis couples equal helicities through both, with cross signed by 2 pol - 1.

Kinds 🔒

Which of the two coupling kinds of a Coupling a polarization pair uses.

Functions

degrees 🔒

Degrees p that tl_vsw_term admits for source (l, m) and destination (lambda, mu), descending in steps of two. formal/Formal/SelectionRules.lean proves this range.

term_bound 🔒

The most terms from from to to: one per admitted degree of each selected kind. Terms of zero weight are left out, so there can be fewer.

terms 🔒

Terms (p, m - mu, weight) of the translation from source (l, m) to destination (lambda, mu): sum weight z_p(k r) P_p^(m - mu) e^(i (m - mu) phi).

tl_vsw_term 🔒

Degree-p coefficient of the coupling of source (l, m) to destination (lambda, -mu) with q = p - cross. Zero unless both Wigner 3j symbols it multiplies, (l lambda p; m mu -m-mu) from rows[0] = Wigner3jRow::new(l, lambda, m, mu) and (l lambda q; 0 0 0) from rows[1] = Wigner3jRow::new(l, lambda, 0, 0), can be nonzero.