sft_wick.expressions — Symbolic Expression Tree

All expression types are frozen dataclasses — immutable and hashable. Uses exact rational arithmetic via fractions.Fraction.

Expr	Base class for all symbolic expressions.
Rational	Exact rational number.
Symbol	A named symbol, possibly with indices.
Propagator	A two-point function C_{ij}(x, x') or R_{ij}(x, x').
Sum	Sum of expressions.
Product	Product of expressions.
SumOverIndex	Summation over a component index: sum_{i=1}^{N} body.
IntegralOver	Integration over a spatial variable: integral d(var) body.
KroneckerDelta	delta_{ij} for component indices.
DiracDelta	delta(x - y) for spatial arguments.
ImaginaryUnit	The imaginary unit \(\mathrm{i}\).
apply_response_phase	Multiply each term by \((-\mathrm{i})^n\) where n is the number of response propagators R in that term.

Custom symbolic expression tree for Wick contraction results.

All expression types are frozen dataclasses (immutable + hashable). Uses exact rational arithmetic via fractions.Fraction.

class sft_wick.expressions.Expr

Bases: ABC

Base class for all symbolic expressions.

abstractmethod to_latex()

Return type:

str

class sft_wick.expressions.Rational(numerator, denominator=1)

Bases: Expr

Exact rational number.

Parameters:

• numerator (int)

• denominator (int)

numerator: int

denominator: int = 1

classmethod from_number(n)

Parameters:

n (int | Fraction)

Return type:

Rational

property is_zero: bool

property is_one: bool

to_fraction()

Return type:

Fraction

to_latex()

Return type:

str

class sft_wick.expressions.Symbol(name, indices=(), spatial_args=())

Bases: Expr

A named symbol, possibly with indices.

Examples

Symbol(‘F’, (‘i’, ‘j’, ‘k’)) -> F_{ijk} Symbol(‘K’, (‘i’, ‘j’), (‘y_0’, ‘y_1’)) -> K_{ij}(y_0, y_1)

Parameters:

• name (str)

• indices (tuple[str, ...])

• spatial_args (tuple[str, ...])

name: str

indices: tuple[str, ...] = ()

spatial_args: tuple[str, ...] = ()

to_latex()

Return type:

str

class sft_wick.expressions.Propagator(kind, index_left, index_right, spatial_left, spatial_right)

Bases: Expr

A two-point function C_{ij}(x, x’) or R_{ij}(x, x’).

For scalar fields, index_left and index_right are None.

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

Parameters:

• kind (str)

• index_left (str | None)

• index_right (str | None)

• spatial_left (str)

• spatial_right (str)

kind: str

index_left: str | None

index_right: str | None

spatial_left: str

spatial_right: str

to_latex()

Return type:

str

class sft_wick.expressions.Sum(terms)

Bases: Expr

Sum of expressions.

Parameters:

terms (tuple[Expr, ...])

terms: tuple[Expr, ...]

to_latex()

Return type:

str

class sft_wick.expressions.Product(factors)

Bases: Expr

Product of expressions.

Parameters:

factors (tuple[Expr, ...])

factors: tuple[Expr, ...]

to_latex()

Return type:

str

class sft_wick.expressions.SumOverIndex(index_name, dimension, body)

Bases: Expr

Summation over a component index: sum_{i=1}^{N} body.

Parameters:

• index_name (str)

• dimension (int)

• body (Expr)

index_name: str

dimension: int

body: Expr

to_latex()

Return type:

str

class sft_wick.expressions.IntegralOver(variable, body)

Bases: Expr

Integration over a spatial variable: integral d(var) body.

Parameters:

• variable (str)

• body (Expr)

variable: str

body: Expr

to_latex()

Return type:

str

class sft_wick.expressions.KroneckerDelta(index1, index2)

Bases: Expr

delta_{ij} for component indices.

Parameters:

• index1 (str)

• index2 (str)

index1: str

index2: str

to_latex()

Return type:

str

class sft_wick.expressions.DiracDelta(arg1, arg2)

Bases: Expr

delta(x - y) for spatial arguments.

Parameters:

• arg1 (str)

• arg2 (str)

arg1: str

arg2: str

to_latex()

Return type:

str

class sft_wick.expressions.ImaginaryUnit

Bases: Expr

The imaginary unit \(\mathrm{i}\).

Used to represent the phase factor \((-\mathrm{i})^n\) that arises from the MSR convention \(\langle\phi\,\psi\rangle \propto -\mathrm{i}\,R\).

to_latex()

Return type:

str

sft_wick.expressions.I = ImaginaryUnit()

Module-level constant for the imaginary unit.

sft_wick.expressions.apply_response_phase(expr)

Multiply each term by \((-\mathrm{i})^n\) where n is the number of response propagators R in that term.

This implements the MSR convention \(\langle\phi(a)\,\psi(b)\rangle = -\mathrm{i}\,R(a,b)\).

The phase is absorbed into the existing rational coefficient so that the factored form of the expression is preserved. For example, \((-\mathrm{i})^3 = \mathrm{i}\) applied to a term with prefactor \(-\tfrac{1}{6}\) yields \(-\tfrac{\mathrm{i}}{6}\).

Parameters:

expr (Expr)

Return type:

Expr