Direction

Enum specifying tensor index orientation.

Direction

Bases: IntEnum

Orientation flag used by tensor indices.

Attributes

IN class-attribute instance-attribute

IN = +1

OUT class-attribute instance-attribute

OUT = -1

Functions

reverse

reverse() -> Direction

Return the opposite orientation (IN ↔ OUT).

Description

The Direction enum specifies whether an index is incoming or outgoing, which determines how charges contribute to conservation laws.

Values

• Direction.IN = -1: Incoming index
• Direction.OUT = 1: Outgoing index

Charge Conservation

Direction affects charge conservation:

∑(OUT charges) - ∑(IN charges) = neutral element

Example with U(1)

# Index 1: OUT, charge = 2
# Index 2: IN, charge = 1  
# Index 3: OUT, charge = -1
# Total: 2 - 1 + (-1) = 0 ✓ (conserved)

Methods

reverse()

Returns the opposite direction:

• Direction.OUT.reverse() → Direction.IN
• Direction.IN.reverse() → Direction.OUT

Physical Interpretation

In quantum physics:

Direction	Represents
OUT	Ket vectors |ψ⟩, creation operators, outgoing states
IN	Bra vectors ⟨ψ|, annihilation operators, incoming states

See Also

• Index: Uses direction
• Sector: Charge-dimension pairs
• Examples: First Tensor

Notes

For contraction, paired indices must have opposite directions. Use Index.flip() to reverse direction without conjugating charges.