sft_wick.simplify — Expression Simplification

Expression simplification for Wick contraction results.

Pipeline: 1. Flatten nested Sum/Product 2. Absorb rational prefactors in products 3. Eliminate zeros 4. Canonical ordering of propagators 5. Term collection (combine like terms) 6. Diagram-based collection (group by Feynman diagram isomorphism)

sft_wick.simplify.simplify(expr)[source]

Main simplification entry point.

Parameters:

expr (Expr)

Return type:

Expr

sft_wick.simplify.collect_by_diagram(expr)[source]

Collect terms whose Feynman diagrams are isomorphic.

Groups terms that represent the same Feynman diagram under relabeling of dummy integration variables and summation indices. Factors out canonical propagators and sums coupling coefficients with appropriately permuted indices.

This correctly handles:

  • Spatial variable relabeling: integration variables can be freely permuted (e.g. y_0 ↔ y_1 at second order).

  • C propagator symmetry: C(x, y) = C(y, x).

  • Coupling permutation: index permutations are applied to the outer coupling symbols, producing a sum of permuted couplings.

Example:

F_{i0 i1 i2} × [R_{a i2}(x,y) C_{i0 i1}(y,y)
                 + R_{a i1}(x,y) C_{i0 i2}(y,y)]

becomes:

(F_{i0 i1 i2} + F_{i0 i2 i1}) × R_{a i2}(x,y) C_{i0 i1}(y,y)
Parameters:

expr (Expr)

Return type:

Expr

sft_wick.simplify.collect_by_topology(expr)

Collect terms whose Feynman diagrams are isomorphic.

Groups terms that represent the same Feynman diagram under relabeling of dummy integration variables and summation indices. Factors out canonical propagators and sums coupling coefficients with appropriately permuted indices.

This correctly handles:

  • Spatial variable relabeling: integration variables can be freely permuted (e.g. y_0 ↔ y_1 at second order).

  • C propagator symmetry: C(x, y) = C(y, x).

  • Coupling permutation: index permutations are applied to the outer coupling symbols, producing a sum of permuted couplings.

Example:

F_{i0 i1 i2} × [R_{a i2}(x,y) C_{i0 i1}(y,y)
                 + R_{a i1}(x,y) C_{i0 i2}(y,y)]

becomes:

(F_{i0 i1 i2} + F_{i0 i2 i1}) × R_{a i2}(x,y) C_{i0 i1}(y,y)
Parameters:

expr (Expr)

Return type:

Expr

sft_wick.simplify.diagonal_propagators(expr, *, diag_R=False, diag_C=False, iso_R=False, iso_C=False)[source]

Enforce diagonal and/or isotropic propagator constraints.

When diag_R=True, response propagators are diagonal: \(R_{ij}(x,y) = \delta_{ij}\,R(x,y)\). This substitutes the constraint \(i = j\) into couplings and propagators, eliminating one summation index per constrained propagator.

When diag_C=True, the same is done for correlation propagators.

When iso_R=True (implies diag_R=True), all diagonal R entries are further assumed equal: \(R_{ii}(x,y) = R(x,y)\). The remaining component index is dropped from R propagators entirely.

When iso_C=True (implies diag_C=True), the same for C.

Parameters:

  • expr (Expr) – Expression to simplify.

  • diag_R (bool) – Enforce diagonal response propagators.

  • diag_C (bool) – Enforce diagonal correlation propagators.

  • iso_R (bool) – Enforce isotropic (index-free) response propagators.

  • iso_C (bool) – Enforce isotropic (index-free) correlation propagators.

Returns:

Simplified expression with the requested constraints applied.

Return type:

Expr