ts-quantum/dist/quantum/src/intertwiner/core.js

TypeScript library for quantum mechanics calculations and utilities

/**
 * Core Intertwiner Space Calculations
 *
 * Fundamental functions for calculating intertwiner space dimensions and
 * validating angular momentum coupling rules in spin network theory.
 */
/**
 * Check if three angular momenta satisfy the triangle inequality.
 * Required for valid angular momentum coupling in quantum mechanics.
 *
 * @param j1 First angular momentum quantum number
 * @param j2 Second angular momentum quantum number
 * @param j3 Third angular momentum quantum number
 * @returns True if triangle inequality is satisfied
 */
export function triangleInequality(j1, j2, j3) {
    return (j1 + j2 >= j3) && (j2 + j3 >= j1) && (j3 + j1 >= j2);
}
/**
 * Calculate allowed intermediate spins when coupling j1 and j2.
 * Returns array of possible j values according to angular momentum addition rules.
 *
 * @param j1 First angular momentum quantum number
 * @param j2 Second angular momentum quantum number
 * @returns Array of allowed intermediate angular momentum values
 */
export function allowedIntermediateSpins(j1, j2) {
    const j_min = Math.abs(j1 - j2);
    const j_max = j1 + j2;
    // Check if j1 + j2 is an integer
    const sumJ = j1 + j2;
    const isIntegerSum = Math.abs(sumJ - Math.round(sumJ)) < 1e-10;
    // Generate all possible intermediate j values (integers or half-integers)
    const step = isIntegerSum ? 1 : 0.5;
    const result = [];
    for (let j = j_min; j <= j_max + 1e-10; j += step) {
        result.push(j);
    }
    return result;
}
/**
 * Calculate the dimension of the intertwiner space for a node with given edge spins.
 * Dispatches to appropriate calculation based on node valence.
 *
 * @param edgeSpins Array of angular momentum quantum numbers for node edges
 * @returns Dimension of the intertwiner space
 */
export function calculateDimension(edgeSpins) {
    const valence = edgeSpins.length;
    switch (valence) {
        case 2:
            // Two-valent: dimension 1 if spins are equal, 0 otherwise
            return Math.abs(edgeSpins[0] - edgeSpins[1]) < 1e-10 ? 1 : 0;
        case 3:
            // Three-valent: dimension 1 if triangle inequality satisfied, 0 otherwise
            const [j1, j2, j3] = edgeSpins;
            return triangleInequality(j1, j2, j3) ? 1 : 0;
        case 4:
            // Four-valent: use full intertwiner dimension calculation
            const [ja, jb, jc, jd] = edgeSpins;
            return intertwinerDimension(ja, jb, jc, jd);
        default:
            console.warn(`Intertwiner dimension calculation for ${valence}-valent nodes not implemented`);
            return 1;
    }
}
/**
 * Calculate the dimension of the intertwiner space for a 4-valent node
 * with edges labeled j1, j2, j3, j4.
 *
 * Uses the recoupling scheme: (j1 ⊗ j2) ⊗ (j3 ⊗ j4) → j = 0
 *
 * @param j1 First edge angular momentum
 * @param j2 Second edge angular momentum
 * @param j3 Third edge angular momentum
 * @param j4 Fourth edge angular momentum
 * @returns Dimension of the intertwiner space
 */
function intertwinerDimension(j1, j2, j3, j4) {
    // Get allowed intermediate spins for each pair
    const j12_values = allowedIntermediateSpins(j1, j2);
    const j34_values = allowedIntermediateSpins(j3, j4);
    // Count overlapping values that can couple to j=0
    let dimension = 0;
    for (const j12 of j12_values) {
        if (j34_values.some(j34 => Math.abs(j12 - j34) < 1e-10)) {
            dimension++;
        }
    }
    return dimension;
}
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