neuralqx.operators.computational.spherical.numba package

class SphericalEx(H, vertex, *, gamma=1.0)

Bases: ComputationalOperator

Diagonal E^x at a single vertex:

E^x_v(σ) = K(v) / 2

with K(v) = k_-(v) + k_+(v). For endpoints, any missing k-edge is treated as 0 so that K(v) sums only the available incident k’s.

Note

  • we do not mod_add the sum K(v)

  • we use an Immirzi parameter of 1.0 by default

class SphericalVolume(H, vertex, *, shift=0.0)

Bases: ComputationalOperator

Diagonal volume factor (single-vertex) in the spherical U(1) reduction:

V_v(σ) = |μ(v)| * sqrt( | K(v) + shift | )

where K(v) = k_-(v) + k_+(v). For endpoints, any missing k-edge is treated as 0 so that K(v) sums only the available incident k’s.

Note: right now we do not mod_add the K(v) + shift.

class SphericalVertexConstraintBojowaldSwiderskiAdjoint(H, vertex, *, include_gamma_terms=True, delta=2, outer_km_constant=0, outer_kp_constant=0, immirzi=1.0)

Bases: ComputationalOperator

A ComputationalOperator implementing the single-vertex Euclidean constraint ( H_v = H_L(v) + H_C(v) + H_R(v) ) at a chosen inner k-vertex (v).

Notes

  • This operator is not Hermitian in this bare Euclidean form. If a Hermitian positive operator is desired, wrap with a squaring construction upstream (e.g., Squared(…)).

  • All overall constants are taken to be absorbed into units with (gamma=1) and (delta=2).

class SphericalVertexConstraintBojowaldSwiderskiAdjointFast(H, vertex, *, include_gamma_terms=True, delta=2, outer_km_constant=0, outer_kp_constant=0, immirzi=1.0)

Bases: ComputationalOperator

This version is an optimised and jax.jit-friendly version of the SphericalVertexConstraintBojowaldSwiderski implementation above.

The implementation is not self-documented, as it aims to mirror the well-documented implementation in the SphericalVertexConstraintBojowaldSwiderski class.

class SphericalVertexConstraintBojowaldSwiderski(H, vertex, *, include_gamma_terms=True, delta=2, outer_km_constant=0, outer_kp_constant=0, immirzi=1.0)

Bases: ComputationalOperator

A ComputationalOperator implementing the single-vertex Euclidean constraint ( H_v = H_L(v) + H_C(v) + H_R(v) ) at a chosen inner k-vertex (v).

Notes

  • This operator is not Hermitian in this bare Euclidean form. If a Hermitian positive operator is desired, wrap with a squaring construction upstream (e.g., Squared(…)).

  • All overall constants are taken to be absorbed into units with (gamma=1) and (delta=2).

class SphericalVertexConstraintBojowaldSwiderskiFast(H, vertex, *, include_gamma_terms=True, delta=2, outer_km_constant=0, outer_kp_constant=0, immirzi=1.0)

Bases: ComputationalOperator

This version is an optimised and jax.jit-friendly version of the SphericalVertexConstraintBojowaldSwiderski implementation above.

The implementation is not self-documented, as it aims to mirror the well-documented implementation in the SphericalVertexConstraintBojowaldSwiderski class.