Pith Number

pith:GWDINWBM

pith:2026:GWDINWBMGJ4HB4X34W7JYFPWVQ

not attested not anchored not stored refs resolved

Central Characters of $G_{\mathrm{NC}}$, Darboux Normalization, and the Kinematical Inequivalence of NCQM and QM

S. Hasibul Hassan Chowdhury

Generic noncommutative quantum mechanics sectors are not unitarily equivalent to ordinary quantum mechanics as G_NC representations

arxiv:2603.00524 v2 · 2026-02-28 · math-ph · math.MP · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GWDINWBMGJ4HB4X34W7JYFPWVQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove that a generic nondegenerate NCQM sector (ℏ₀,ϑ₀,B₀), with ℏ₀,ϑ₀,B₀≠0 and ℏ₀−B₀ϑ₀≠0, is not unitarily equivalent to the ordinary QM sector (ℏ₀,0,0) as a G_NC-representation.

C2weakest assumption

That the kinematical symmetry group is correctly identified as the step-two nilpotent Lie group G_NC with three-dimensional center whose regular unitary dual is labelled by central characters (ℏ,ϑ,B_in), and that ordinary QM corresponds exactly to the inflated Weyl-Heisenberg representations with central character (ℏ,0,0).

C3one line summary

Generic nondegenerate NCQM sectors with nonzero central character parameters are not unitarily equivalent to ordinary QM as representations of G_NC.

References

14 extracted · 14 resolved · 7 Pith anchors

[1] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Sternheimer,Deformation theory and quantization. I. Deformations of symplectic structures, Annals Phys.111(1978) 61–110 1978

[2] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Sternheimer,Deformation theory and quantization. II. Physical applications, Annals Phys.111(1978) 111–151 1978

[3] On Quantum Mechanics on Noncommutative Quantum Phase Space 2004 · arXiv:hep-th/0309006

[4] Noncommutative Quantum Mechanics and Seiberg-Witten Map 2004 · arXiv:hep-th/0401180

[5] A comparative review of four formulations of noncommutative quantum mechanics 2016 · arXiv:1603.07176

Cited by

1 paper in Pith

From Noncommutative Kinematics to $U(1)_{\star}$ Gauge Theory: A Family of Spectral Triples with Localized Gauge-induced Perturbations

Receipt and verification

First computed	2026-05-18T03:10:03.501505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

358686d82c327870f2fbe5be9c15f6ac21eedf77820ca159c3ca4001bdb93df5

Aliases

arxiv: 2603.00524 · arxiv_version: 2603.00524v2 · doi: 10.48550/arxiv.2603.00524 · pith_short_12: GWDINWBMGJ4H · pith_short_16: GWDINWBMGJ4HB4X3 · pith_short_8: GWDINWBM

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GWDINWBMGJ4HB4X34W7JYFPWVQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 358686d82c327870f2fbe5be9c15f6ac21eedf77820ca159c3ca4001bdb93df5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86b9820d1fc9801348b9507402901509c16ab698c1362d5e1a82999266371bf7",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-02-28T07:49:53Z",
    "title_canon_sha256": "29aa68a676ea8ba7cfe62df3389d0202977e35e0cb2eda5677a0697338489de7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.00524",
    "kind": "arxiv",
    "version": 2
  }
}