Sector

Charge sector descriptor pairing a charge with a dimension.

Sector dataclass

Sector(charge: Charge, dim: int)

Charge sector descriptor pairing a conserved charge with its dimension.

Attributes:

Name	Type	Description
charge	Charge	The conserved quantity carried by the sector. May be any hashable value.
dim	int	Positive integer indicating how many states/multiplets the sector spans.

Attributes

charge instance-attribute

charge: Charge

dim instance-attribute

dim: int

Description

A Sector represents a symmetry sector within an index, containing:

• charge: The conserved quantum number (type depends on symmetry group)
• dim: Number of states in this sector (positive integer)

Sectors are immutable frozen dataclasses.

Charge Types by Group

Group	Charge Type	Examples
U1Group	int	-2, -1, 0, 1, 2
Z2Group	int (0 or 1)	0, 1
SU2Group	int ≥ 0 (2j convention)	0, 1, 2, 3 (spins 0, 1/2, 1, 3/2)
ProductGroup	tuple	(2, 1), (0, 0)

Validation

Sectors validate at construction:

• Dimension must be positive
• Charge must be valid for the group
• No duplicate charges allowed within an index

See Also

• Index: Uses sectors to define structure
• Direction: Index orientation
• U1Group: Integer charges
• Z2Group: Binary charges
• SU2Group: Spin charges (2j convention)
• Examples: First Tensor