Pith. Sign in

RECORD

Fock space representations of Bogolyubov transformations as spin representations

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
K. Neerg{aa}rd

Nuclear Theory · Submitted 16 Dec 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The representation on a Fock space of the group of Bogolyubov transformations is recognized as the spin representation of an orthogonal group.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2212.08598 (version 4)
Pith IDOSQECXIF, Pith's permanent record of this paper and its review
CitationK. Neerg{\aa}rd. "Fock space representations of Bogolyubov transformations as spin representations." arXiv:2212.08598 (2022). https://pith.science/paper/OSQECXIF
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,354 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.89 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

The representation on a Fock space of the group of Bogolyubov transformations is recognized as the spin representation of an orthogonal group. Derivations based on this observation of some known formulas for the overlap amplitude of two Bogolyubov quasi-fermion vacuum states that are in some cases more complete than those in the literature are shown. It is pointed out that the name of an "Onishi formula" is assigned in the literature to two different expressions which are related but have different scopes. One of them has what has been described as a sign problem, the other one, due to Onishi and Yoshida, has a more limited scope and no sign problem. I give a short proof of the latter, whose derivation is missing in the paper by Onishi and Yoshida, and a new, combinatoric, proof of an equivalent formula recently derived by Robledo.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The representation on a Fock space of the group of Bogolyubov transformations is recognized as the spin representation of an orthogonal group. background 0.81 0.13 0.69 asserted 1.00
s1 Derivations based on this observation of some known formulas for the overlap amplitude of two Bogolyubov quasi-fermion vacuum states that are in some cases more complete than those in the literature are shown. contribution 0.89 0.87 0.17 asserted 1.00
s2 It is pointed out that the name of an "Onishi formula" is assigned in the literature to two different expressions which are related but have different scopes. background 0.47 0.24 0.08 asserted 1.00
s3 One of them has what has been described as a sign problem, the other one, due to Onishi and Yoshida, has a more limited scope and no sign problem. background 0.89 0.10 0.07 asserted 1.00
s4 I give a short proof of the latter, whose derivation is missing in the paper by Onishi and Yoshida, and a new, combinatoric, proof of an equivalent formula recently derived by Robledo. contribution 1.00 0.95 0.14 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The representation on a Fock space of the group of Bogolyubov transformations is recognized as the spin representation of an orthogonal group. Derivations based on this observation of some known formulas for the overlap amplitude of two Bogolyubov quasi-fermion vacuum states that are in some cases more complete than those in the literature are shown. It is pointed out that the name of an "Onishi formula" is assigned in the literature to two different expressions which are related but have different scopes. One of them has what has been described as a sign problem, the other one, due to Onishi and Yoshida, has a more limited scope and no sign problem. I give a short proof of the latter, whose derivation is missing in the paper by Onishi and Yoshida, and a new, combinatoric, proof of an equivalent formula recently derived by Robledo.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.