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Umbral methods and operator ordering

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D. Babusci, G. Dattoli

Mathematical Physics · Submitted 7 Dec 2011

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

The authors' main claim By using methods of umbral nature, we discuss new rules concerning the operator ordering.

how it is stated · asserted 0.98 read the record →

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arXiv ID1112.1570 (version 1)
Pith IDH4SNIEFC, Pith's permanent record of this paper and its review
CitationD. Babusci, G. Dattoli. "Umbral methods and operator ordering." arXiv:1112.1570 (2011). https://pith.science/paper/H4SNIEFC
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,802 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. The usefulness of the obtained results in quantum field theory is discussed.

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 By using methods of umbral nature, we discuss new rules concerning the operator ordering. contribution 0.98 0.90 0.38 asserted 0.98
s1 We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. method 0.99 0.87 0.07 asserted 0.98
s2 The usefulness of the obtained results in quantum field theory is discussed. interpretation 0.96 0.62 0.19 asserted 0.57

What kind of paper the classifier reports this is: method or tool 0.51 · evidence from proof or derivation 0.99.

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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

By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. The usefulness of the obtained results in quantum field theory is discussed.

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2 arXiv papers cite this in 4 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

Builds on it 1 paper
  • In this paper we reconsider the operator-ordering problem for pseudo-evolutionary problems in more general terms than those considered in [ref] , and we address the time-ordering problem by discussing the possibility of adapting for this purpose the use of expansions such as the Volterra-Neumann or Feynman-Dyson series [ref] .

    Operator Ordering and Solution of Pseudo-Evolutionary Equations · Introduction · 0.81

Uses its method or tool 2 papers
  • We will outline the procedure allowing the merging of ordering procedures and umbral image type methods, using as a reference example the so-called “Laguerre-calculus” along the lines of [ref] .

    Operator Ordering and Solution of Pseudo-Evolutionary Equations · Laguerre derivative, Laguerre exponential and operator-ordering · 0.90

  • Let us consider an evolution equation of the form [equation] The relevant procedure for combining differential calculus with the umbral formalism is described in [ref] .

    Dual Numbers and Operational Umbral Methods · Weyl formula and modified Hermite polynomials · 0.91

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