MomentumSignature

Symbolica documentation for getting started, symbolic expressions, numerical evaluation, pattern matching, and APIs in Python and Rust.

`MomentumSignature`

class MomentumSignature

Integer coefficients expressing one edge momentum in a chosen basis.

A signature separates coefficients of independent loop momenta from those of external momenta, for example -l1 + p2.

Examples

from symbolica import S, E
from symbolica.community import hepkit as hep
model = hep.Model.phi4()
process = model.process(["phi", "phi"], ["phi", "phi"])
result = process.generate_diagrams(loops=1)
diagram = result.diagrams[0]
basis = diagram.loop_momentum_basis
edge_id = basis.loop_edges[0]
signature = basis.edge_signatures[edge_id]
routing = signature.format_momentum()

Attributes

Name	Description
`external`	Return the integer coefficients of the external momenta.
`loops`	Return the integer coefficients of the independent loop momenta.

`external`

MomentumSignature.external: builtins.list[builtins.int]

Return the integer coefficients of the external momenta.

Examples

Using the setup in the MomentumSignature class example:

external_coefficients = signature.external

`loops`

MomentumSignature.loops: builtins.list[builtins.int]

Return the integer coefficients of the independent loop momenta.

Examples

Using the setup in the MomentumSignature class example:

assert len(signature.loops) == diagram.loop_count

Methods

Name	Description
`__repr__`	Return an unambiguous momentum-signature summary.
`__str__`	Return the conventional momentum sum for `str(signature)`.
`_repr_pretty_`	Write the momentum signature to an IPython pretty printer.
`format_momentum`	Format the signature as a conventional momentum sum.
`integer_coefficients`	Return loop and external coefficients as a pair of integer lists.

`repr`

MomentumSignature.__repr__() -> builtins.str

Return an unambiguous momentum-signature summary.

Examples

Using the setup in the MomentumSignature class example:

edge_id, signature = next(iter(basis.edge_signatures.items()))
print(f"edge {edge_id}: {signature!r}")

`str`

MomentumSignature.__str__() -> builtins.str

Return the conventional momentum sum for str(signature).

Examples

Using the setup in the MomentumSignature class example:

signature = next(iter(basis.edge_signatures.values()))
print(f"propagator momentum: {signature}")

`_repr_pretty_`

MomentumSignature._repr_pretty_(pretty: typing.Any, cycle: builtins.bool) -> None

Write the momentum signature to an IPython pretty printer.

Examples

Using the setup in the MomentumSignature class example:

from IPython.lib.pretty import pretty
text = pretty(signature)

Parameters

pretty (Any) The IPython pretty-printer object.
cycle (bool) Whether this object is part of a recursive formatting cycle.

`format_momentum`

MomentumSignature.format_momentum() -> builtins.str

Format the signature as a conventional momentum sum.

Examples

Using the setup in the MomentumSignature class example:

Print the momentum routing assigned to every propagator:

for edge_id, signature in basis.edge_signatures.items():
    print(edge_id, signature.format_momentum())

`integer_coefficients`

MomentumSignature.integer_coefficients() -> tuple[builtins.list[builtins.int], builtins.list[builtins.int]]

Return loop and external coefficients as a pair of integer lists.

Examples

Using the setup in the MomentumSignature class example:

signature = next(iter(basis.edge_signatures.values()))
loops, external = signature.integer_coefficients()
print("loop coefficients:", loops, "external coefficients:", external)