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Direction

Arrow direction for tensor network edges.

Direction

Arrow direction for a tensor network edge: incoming (+1) or outgoing (-1).

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

Examples:

>>> import yuzuha
>>> d = yuzuha.Direction.incoming()
>>> print(d.sign())
1
>>> print(d.flip())
Direction.outgoing

incoming staticmethod 

incoming() -> Direction

Create an incoming Direction (sign = +1).

Returns:

Type Description
Direction

An incoming direction.

outgoing staticmethod 

outgoing() -> Direction

Create an outgoing Direction (sign = -1).

Returns:

Type Description
Direction

An outgoing direction.

from_sign staticmethod 

from_sign(sign: int) -> Direction

Create a Direction from its sign value.

Parameters:

Name Type Description Default
sign int

+1 for incoming, -1 for outgoing.

 required

Returns:

Type Description
Direction

The corresponding Direction.

Raises:

Type Description
ValueError

If sign is not +1 or -1.

sign 

sign() -> int

Return the numerical sign of this direction.

Returns:

Type Description
int

+1 for incoming, -1 for outgoing.

flip 

flip() -> Direction

Return the opposite Direction.

Returns:

Type Description
Direction

The flipped direction.

is_incoming 

is_incoming() -> bool

Return True if this direction is incoming.

Returns:

Type Description
bool

True if incoming.

is_outgoing 

is_outgoing() -> bool

Return True if this direction is outgoing.

Returns:

Type Description
bool

True if outgoing.

Description

Direction is a two-valued enum that specifies whether an external edge is incoming (primal representation) or outgoing (dual representation). Arrow directions govern how charges fuse and how the invariant metric is applied when reversing an arrow.

from yuzuha import Direction

d_in  = Direction.Incoming   # primal / ket-type index
d_out = Direction.Outgoing   # dual / bra-type index

In the sign convention used throughout Yuzuha:

  • An incoming edge with spin \(j\) contributes a factor of \(+1\) to the total magnetic quantum number sum.
  • An outgoing edge with spin \(j\) contributes a factor of \(-1\).

Charge conservation then requires that the total signed magnetic quantum number of all edges is zero:

\[\sum_{\text{incoming}} m_i - \sum_{\text{outgoing}} m_j = 0\]

Arrow reversal from incoming to outgoing is implemented via the metric tensor \(g\). Arrow reversal from outgoing to incoming uses \(g^{-1} = (-1)^{2j}\, g\), which is \(+g\) for integer spins and \(-g\) for half-integer spins.

See Also

Notes

Direction values are comparable and can be passed directly to Edge.incoming / Edge.outgoing constructors. The .flip() method (if available on the Rust type) is accessible from Python as Edge.with_flipped_direction().