Z2Group

Z(2) symmetry group with binary charges.

Z2Group dataclass

Z2Group()

Bases: AbelianGroup

Z2 with charges 0/1 (parity).

Attributes

name property

name: str

neutral property

neutral: int

Functions

dual

dual(q: int) -> int

fuse_unique

fuse_unique(*qs: int) -> int

equal

equal(a: int, b: int) -> bool

validate_charge

validate_charge(q: Any) -> None

Ensure a charge is a valid Z2 parity (0 or 1).

Description

Represents discrete Z(2) symmetry. Charges are 0 or 1, representing binary quantum numbers.

Charge Operations

• Fusion: XOR (q1 ⊕ q2)
• Dual: Self-dual (0→0, 1→1)
• Identity: 0

Physical Applications

• Fermion parity (even/odd number)
• Spatial inversion symmetry
• Time-reversal (in some contexts)

See Also

• U1Group: Integer charge symmetry
• ProductGroup: Multiple symmetries
• Overview: Symmetry system introduction
• Examples: Z2

Notes

Only charges 0 and 1 are valid. Other values raise ValueError.