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Superanalogs of symplectic and contact geometry and their applications to quantum field theory

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Albert Schwarz

High Energy Physics - Theory · Submitted 17 Jun 1994

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

The authors' main claim It is shown that this generalization can be used to obtain some important results in quantum field theory.

how it is stated · asserted 0.97 read the record →

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arXiv IDhep-th/9406120 (version 1)
Pith IDVWTQFCJ7, Pith's permanent record of this paper and its review
CitationAlbert Schwarz. "Superanalogs of symplectic and contact geometry and their applications to quantum field theory." arXiv:hep-th/9406120 (1994). https://pith.science/paper/VWTQFCJ7
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,557 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.57 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in quantum field theory. In particular, regarding $N$-superconformal geometry as particular case of contact complex geometry, one can better understand $N=2$ superconformal field theory and its connection to topological conformal field theory. The odd symplectic geometry constitutes a mathematical basis of Batalin-Vilkovisky procedure of quantization of gauge theories. The exposition is based mostly on published papers. However, the paper contains also a review of some unpublished results (in the section devoted to the axiomatics of $N=2$ superconformal theory and topological quantum field theory). The paper will be published in Berezin memorial volume.

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 paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. background 0.81 0.19 0.05 asserted 0.99
s1 It is shown that this generalization can be used to obtain some important results in quantum field theory. result 0.72 0.72 0.68 asserted 0.97
s2 In particular, regarding $N$-superconformal geometry as particular case of contact complex geometry, one can better understand $N=2$ superconformal field theory and its connection to topological conformal field theory. interpretation 0.47 0.44 0.23 hedged possibility 0.77
s3 The odd symplectic geometry constitutes a mathematical basis of Batalin-Vilkovisky procedure of quantization of gauge theories. background 0.81 0.11 0.10 asserted 1.00
s4 The exposition is based mostly on published papers. method 0.78 0.16 0.02 asserted 0.98
s5 However, the paper contains also a review of some unpublished results (in the section devoted to the axiomatics of $N=2$ superconformal theory and topological quantum field theory). contribution 0.87 0.69 0.02 asserted 1.00
s6 The paper will be published in Berezin memorial volume. background 0.93 0.08 0.02 asserted 0.98

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
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 paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in quantum field theory. In particular, regarding $N$-superconformal geometry as particular case of contact complex geometry, one can better understand $N=2$ superconformal field theory and its connection to topological conformal field theory. The odd symplectic geometry constitutes a mathematical basis of Batalin-Vilkovisky procedure of quantization of gauge theories. The exposition is based mostly on published papers. However, the paper contains also a review of some unpublished results (in the section devoted to the axiomatics of $N=2$ superconformal theory and topological quantum field theory). The paper will be published in Berezin memorial volume.

Human review

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References
How the literature uses it

2 arXiv papers cite this in 3 sentences

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

Papers citing it · 1 sentence without a confident label

Compares with it 1 paper
  • This should be compared with the Darboux theorem in symplectic supergeometry, see for example Schwarz [ref] , proofs of which are sketched by Kostant [ref] and Shander [ref] .

    Symplectic $\mathbb{Z}_2^n$-manifolds · The $_2^n$-graded Darboux theorem · 1.00

Cites it as background 1 paper
  • In particular, the category of supermanifolds allows for even and odd symplectic structures, the latter being vital in the BV-BRST formalism (see [ref] ).

    Symplectic $\mathbb{Z}_2^n$-manifolds · Introduction · 0.94

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