Spin

Irreducible representation label for SU(2).

Spin

Spin(j_doubled: int)

SU(2) irreducible representation label, stored as doubled integer 2j.

Parameters:

Name	Type	Description	Default
j_doubled	int	The doubled spin value 2j. Must be a non-negative integer.	required

Raises:

Type	Description
ValueError	If j_doubled is negative.

Examples:

>>> import yuzuha
>>> j_half = yuzuha.Spin(1)   # j = 1/2
>>> j1     = yuzuha.Spin(2)   # j = 1
>>> print(j_half.value())
0.5
>>> print(j1.dimension())
3

value

value() -> float

Return the spin as a float j = j_doubled / 2.

Returns:

Type	Description
float	The spin value j.

twice

twice() -> int

Return the internal doubled integer 2j.

Returns:

Type	Description
int	The doubled spin value.

dimension

dimension() -> int

Return the representation dimension 2j + 1.

Returns:

Type	Description
int	The number of magnetic quantum number states.

is_integer

is_integer() -> bool

Return True if j is a non-negative integer.

Returns:

Type	Description
bool	True for integer spin, False for half-integer spin.

is_half_integer

is_half_integer() -> bool

Return True if j is a strict half-integer.

Returns:

Type	Description
bool	True for half-integer spin, False for integer spin.

Description

Spin represents an SU(2) irreducible representation by its spin quantum number \(j \in \{0, \frac{1}{2}, 1, \frac{3}{2}, \ldots\}\). Internally, spins are stored as doubled integers \(2j\) to avoid floating-point arithmetic throughout all computations.

The constructor takes the doubled spin value as an integer argument:

import yuzuha

j0    = yuzuha.Spin(0)   # j = 0
jhalf = yuzuha.Spin(1)   # j = 1/2
j1    = yuzuha.Spin(2)   # j = 1
j32   = yuzuha.Spin(3)   # j = 3/2

Properties

• value() — spin as a Python float (\(j = n/2\))
• twice() — internal doubled integer \(2j\)
• dimension() — representation dimension \(2j + 1\)
• is_integer() — True if \(j\) is a non-negative integer
• is_half_integer() — True if \(j\) is a strict half-integer

See Also

• Edge: Combines a Spin with a Direction
• CGSpec: Specifies a full CG tensor from a list of Edge values
• Yuzuha Protocol — Type System: Abstract RepLabel specification that Spin implements for SU(2)

Notes

Spin values are immutable. Equality, hashing, and < ordering are all supported: Spin objects can be used as dictionary keys and in sets, and lists of spins can be passed to sorted() directly without a key function.

The identity representation is Spin(0) (\(j = 0\)), which has dimension 1 and contributes a trivial factor in all coupling coefficients.