sft_wick.propagators — Propagator Contraction Rules

Propagator contraction rules for MSR field theory.

Defines how pairs of field operators contract:

<phi_i(x) phi_j(x’)>_{S_0} = C_{ij}(x, x’) <phi_i(x) psi_j(x’)>_{S_0} = R_{ij}(x, x’) <psi_i(x) psi_j(x’)>_{S_0} = 0

sft_wick.propagators.contract_pair(op1, op2, ito=True)[source]

Contract two field operators and return the propagator, or None if it vanishes.

Convention for R: physical field index/position is always on the left. R_{ij}(x, x’) = <phi_i(x) psi_j(x’)>_{S_0}

Parameters:

  • op1 (FieldOperator) – First field operator.

  • op2 (FieldOperator) – Second field operator.

  • ito (bool) – If True, the Itô prescription \(\Theta(0)=0\) is applied: the response propagator vanishes at equal spatial points, i.e. \(R(x,x)=0\). This eliminates diagrams with equal-point response contractions (e.g. intra-vertex tadpoles in local vertices).

Returns:

A Propagator, or None if the contraction vanishes.

Return type:

Propagator | None