Edge¶

A directed representation — one edge of a CG tensor.

Edge ¶

One external edge of a CG tensor: a spin paired with a direction.

Use the static constructors incoming() and outgoing() rather than instantiating directly.

Examples:

>>> import yuzuha
>>> j = yuzuha.Spin(1)
>>> e_in  = yuzuha.Edge.incoming(j)
>>> e_out = yuzuha.Edge.outgoing(j)

incoming `staticmethod` ¶

incoming(spin: Spin) -> Edge

Create an incoming edge with the given spin.

Parameters:

Name	Type	Description	Default
`spin`	`Spin`	The spin quantum number for this edge.	required

Returns:

Type	Description
`Edge`	An incoming edge.

outgoing `staticmethod` ¶

outgoing(spin: Spin) -> Edge

Create an outgoing edge with the given spin.

Parameters:

Name	Type	Description	Default
`spin`	`Spin`	The spin quantum number for this edge.	required

Returns:

Type	Description
`Edge`	An outgoing edge.

Description¶

Edge combines a Spin and a Direction to describe a single external edge of a CG tensor. All edges of a CGSpec are specified as a list of Edge values.

The two class-method constructors are the primary way to create edges:

import yuzuha

j = yuzuha.Spin(1)   # j = 1/2

e_in  = yuzuha.Edge.incoming(j)   # spin-1/2 incoming edge
e_out = yuzuha.Edge.outgoing(j)   # spin-1/2 outgoing edge

Fields¶

Attribute	Type	Description
`spin`	`Spin`	Representation label
`direction`	`Direction`	Incoming or outgoing

Derived Quantities¶

Dimension: spin.dimension() — the number of magnetic quantum number states (\(2j + 1\))

Notes¶

Edge objects are immutable and hashable. They can be created from Direction and Spin separately or via the convenience constructors shown above.

Arrow flipping (converting an incoming edge to an outgoing edge of the same spin, or vice versa) requires applying the metric tensor — see use_as_incoming / use_as_outgoing — rather than simply swapping the direction field.