Pith Number

pith:KNZAE2R6

pith:2026:KNZAE2R6ITELMIRIO6VS4Y4LBT

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The Derivation of Phase-Space Metric in a Geometric Quantization Approach: General Relativity with Quantized Phase-Space Metric and Relative Spacetime

A. Alshehri (Egyptian Ctr. Theor. Phys., Ahram Canadian U., Berhampur, Cairo, Cairo), Cairo) A. Tawfik (Islamic U. Madinah, D. Mukherjee (IISER, Egyptian Ctr. Theor. Phys., Hafr El Batin), Hafr El Batin U., K. Mubaidin (Egyptian Ctr. Theor. Phys., M. Nasar (Benha U, S. O. Allehabi (Islamic U. Madinah), WLCAPP

Geometric quantization extends general relativity by deriving a quantized eight-dimensional phase-space metric that produces a relative spacetime.

arxiv:2602.13219 v2 · 2026-01-23 · physics.gen-ph

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Claims

C1strongest claim

The derivation of a quantized eight-dimensional metric tensor is not only presented, but also the implications of it and the corresponding relative spacetime are examined.

C2weakest assumption

That generalizing the four-dimensional Riemann manifold to an eight-dimensional phase-space manifold via geometric quantization and equating line elements produces a consistent quantized metric without introducing unstated inconsistencies or requiring further approximations.

C3one line summary

Derives a quantized eight-dimensional phase-space metric tensor incorporated into general relativity, yielding a relative spacetime.

References

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[1] The canonically conjugate quantitiesx µ 0 andp ν 0 under the fundamental tensorg µν satisfy the noncommutative relation [ˆxµ 0 ,ˆpν 0] =iℏg µν, where ˆpµ 0 =−iℏ∂/∂x 0µ [19, 42, 43]

[2] andp µ = p0 0, pi 0 (1 +βp ρ 0pρ 0) , wherex 0 0 andp 0 0 are the temporal position operator and the 0-th momentum operator, respectively [27, 43]. The stress-energy tensor for quantum particles in cu

[3] (20), so thatF 2(xµ 0 , pν

[4] leads to Eq. (21). From Eq. (21), it is found that, even if the constraint of a quadratic line element is not diminished, Finsler geometry still bears similarities to Riemann geometry. Thus, the metri

[5] This presumes that the functionϕ(p) = 1 +βp ρ 0p0ρ is obviously homogeneous of degree zero inp 0

Cited by

1 paper in Pith

Reevaluation of Inflationary Dynamics in Extended General Relativity with Perturbatively and Tensorially Structured Conformal Metric

Receipt and verification

First computed	2026-05-17T23:39:04.433412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5372026a3e44c8b6222877ab2e638b0ccc9406386b7c8b7a2e6d8efe8b90d602

Aliases

arxiv: 2602.13219 · arxiv_version: 2602.13219v2 · doi: 10.48550/arxiv.2602.13219 · pith_short_12: KNZAE2R6ITEL · pith_short_16: KNZAE2R6ITELMIRI · pith_short_8: KNZAE2R6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KNZAE2R6ITELMIRIO6VS4Y4LBT \
  | 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: 5372026a3e44c8b6222877ab2e638b0ccc9406386b7c8b7a2e6d8efe8b90d602

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afa4cac4de6a55433061c72e9e2093c00a17014203bd6b8cecfd456a5eb67403",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.gen-ph",
    "submitted_at": "2026-01-23T22:04:06Z",
    "title_canon_sha256": "a15d3869a0c4a641c932fbf056761476e68d16d4b5bd041178568152460b3ee3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.13219",
    "kind": "arxiv",
    "version": 2
  }
}