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feat: lift angular momentum to Hilbert space - #1673

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jstoobysmith merged 3 commits into
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lizr-phys:feat/angular-momentum-hilbert-operator
Sep 22, 2026
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jstoobysmith merged 3 commits into
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lizr-phys:feat/angular-momentum-hilbert-operator

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Lift the existing Schwartz-space angular momentum components L_ij = x_i p_j - x_j p_i to partially defined linear operators on SpaceDHilbertSpace d, with domain SchwartzSubmodule d.

The construction transports the existing operator 𝐋 i j through schwartzEquiv volume and schwartzIncl volume, preserving the current Schwartz-space API.

This PR adds application and almost-everywhere bridge lemmas, proves that the operator preserves the Schwartz submodule and has dense domain, and establishes symmetry and the corresponding Physlib IsUnbounded result. The symmetry proof uses the canonical commutation relation together with the existing position and momentum inner-product identities.

AI assistance: Codex (GPT-6 Astra).

Co-authored-by: GPT-6 Astra <noreply@openai.com>
@github-actions github-actions Bot added the small label Sep 22, 2026
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@github-actions github-actions Bot added the t-quantum-mechanics Quantum mechanics label Sep 22, 2026
rfl

/-- Angular momentum on the Schwartz domain is densely defined and closable. -/
lemma angularMomentumHilbertOperator_isUnbounded :

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I think I would put all of these results under angularMomentumOperator if possible, and in that file not in Commutation

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Thanks! I’ve updated this accordingly — the angular-momentum-specific results are now organized around angularMomentumOperator and moved into AngularMomentum.lean.

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There is also a merge conflict on this PR

awaiting-author

@github-actions github-actions Bot added the awaiting-author A reviewer has asked the author a question or requested changes label Sep 22, 2026
Use angularMomentumCLM for Schwartz components and angularMomentumOperator
for the Hilbert-space operator, following the position and momentum APIs.
Move angular momentum symmetry and commutation results into AngularMomentum,
leaving shared commutation infrastructure in Commutation. Update the direct
downstream references and API map without changing mathematical statements
or proofs beyond the renamed identifiers.

AI assistance: Codex (GPT-6 Astra).

Co-authored-by: GPT-6 Astra <noreply@openai.com>
@github-actions github-actions Bot added medium and removed small labels Sep 22, 2026
Keep upstream's positionCLM_inner and momentumCLM_inner lemmas and adapt
the angular momentum symmetry proof to their Hilbert-space statements.
Preserve the angular momentum API organization and upstream commutation
additions while adopting upstream's Lean 4.34 toolchain and dependencies.

AI assistance: Codex (GPT-6 Astra).

Co-authored-by: GPT-6 Astra <noreply@openai.com>

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I've approved this. This looks good to me. Many thanks. Assuming it passes the linters, I will merge shortly.

@jstoobysmith jstoobysmith added ready-to-merge This PR is approved and will be merged shortly and removed awaiting-author A reviewer has asked the author a question or requested changes labels Sep 22, 2026
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jstoobysmith merged commit 5ad56e2 into leanprover-community:master Sep 22, 2026
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