feat: implement compute_wigner_angles()

docs/usage/helicity/spin-alignment.ipynb

@@ -661,7 +661,23 @@
     "\n",
     "for state_id in topology.outgoing_edge_ids:\n",
     "    expr = compute_wigner_rotation_matrix(topology, momenta, state_id)\n",
-    "    display(expr)\n"
+    "    display(expr)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from ampform.kinematics import compute_wigner_angles\n",
+    "\n",
+    "for state_id in topology.outgoing_edge_ids:\n",
+    "    angle_definitions = compute_wigner_angles(topology, momenta, state_id)\n",
+    "    for name, expr in angle_definitions.items():\n",
+    "        angle_symbol = sp.Symbol(name)\n",
+    "        latex = sp.multiline_latex(angle_symbol, expr, environment=\"eqnarray\")\n",
+    "        display(Math(latex))"
    ]
   }
  ],

src/ampform/kinematics.py

@@ -21,7 +21,10 @@
     is_opposite_helicity_state,
     list_decay_chain_ids,
 )
-from ampform.helicity.naming import get_helicity_angle_label
+from ampform.helicity.naming import (
+    get_helicity_angle_label,
+    get_helicity_suffix,
+)
 from ampform.sympy import (
     UnevaluatedExpression,
     _implement_latex_subscript,
@@ -749,6 +752,34 @@ def compute_invariant_masses(
     return invariant_masses
 
 
+def compute_wigner_angles(
+    topology: Topology, momenta: "FourMomenta", state_id: int
+) -> Dict[str, sp.Expr]:
+    """Create an `~sympy.core.expr.Expr` for each angle in a Wigner rotation.
+
+    Implementation of (B.2-4) in
+    :cite:`marangottoHelicityAmplitudesGeneric2020`, with :math:`x'_z` etc.
+    taken from the result of :func:`compute_wigner_rotation_matrix`.
+    """
+    wigner_rotation_matrix = compute_wigner_rotation_matrix(
+        topology, momenta, state_id
+    )
+    x_z = ArraySlice(wigner_rotation_matrix, (slice(None), 1, 3))
+    y_z = ArraySlice(wigner_rotation_matrix, (slice(None), 2, 3))
+    z_x = ArraySlice(wigner_rotation_matrix, (slice(None), 3, 1))
+    z_y = ArraySlice(wigner_rotation_matrix, (slice(None), 3, 2))
+    z_z = ArraySlice(wigner_rotation_matrix, (slice(None), 3, 3))
+    alpha = sp.atan2(z_y, z_x)
+    beta = sp.acos(z_z)
+    gamma = sp.atan2(y_z, -x_z)
+    suffix = get_helicity_suffix(topology, state_id)
+    return {
+        f"alpha{suffix}": alpha,
+        f"beta{suffix}": beta,
+        f"gamma{suffix}": gamma,
+    }
+
+
 def compute_wigner_rotation_matrix(
     topology: Topology, momenta: "FourMomenta", state_id: int
 ) -> MatrixMultiplication: