Angular Momentum

Angular Momentum (V.D118) is the τ-categorical Angular-Momentum Character: the cohomology-class-valued quantity that records a defect bundle's net rotation around the τ-base, equal to ℏ times the integer winding plus possibly half-integer corrections from spin (IV.T17).

Categorical invariant. AngularMomentum(B) := τ-character ω(B) ∈ H¹(τ-base) measuring B's net rotational winding; an E1 invariant.

Primary registry anchor: V.D118

Supporting items: IV.T17, IV.D294, V.D124

1. I.K0 — Universe Postulate establishes τ
2. IV.D11 — Physical Quantity Template — dimensional invariants
3. V.D118 — Angular Momentum Character := rotational-winding cohomology class
4. IV.D294 — Planck's constant in relational units fixes ℏ as the angular-momentum quantum
5. IV.T17 — Emergence of Spin-1/2 — half-integer correction from defect topology

Lean modules referenced: TauLib.BookV.Temporal.BaseCircle, TauLib.BookI.Kernel.ActionQuantum

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. ℏ via IV.D294
3. L = nℏ (integer or half-integer multiple)

Manuscript reference: manuscript-sources/book-05/part05-extended-states/ch-angular-momentum.tex

Status: Formalized

Module: TauLib.BookI.Kernel.ActionQuantum

Lean kind: def

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-Q19-action-space Action (Crossing-Point Action Space)

Referenced by

• PG-Q26-spin Spin (Intrinsic Angular Momentum)