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Dimensional regularization of nonlinear sigma models on a finite time interval

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F. Bastianelli, O. Corradini, P. van Nieuwenhuizen

High Energy Physics - Theory · Submitted 4 Aug 2000

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

The authors' main claim Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'') dimensional regularization requires only a covariant finite two-loop counterterm.

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arXiv IDhep-th/0008045 (version 2)
Pith IDVREBYKXM, Pith's permanent record of this paper and its review
CitationF. Bastianelli, O. Corradini, P. van Nieuwenhuizen. "Dimensional regularization of nonlinear sigma models on a finite time interval." arXiv:hep-th/0008045 (2000). https://pith.science/paper/VREBYKXM
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,899 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.12 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'') dimensional regularization requires only a covariant finite two-loop counterterm. This counterterm is nonvanishing and given by R/8.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We extend dimensional regularization to the case of compact spaces. contribution 0.99 0.93 0.16 asserted 1.00
s1 Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'') dimensional regularization requires only a covariant finite two-loop counterterm. result 0.58 0.66 0.59 asserted 1.00
s2 This counterterm is nonvanishing and given by R/8. result 1.00 0.85 0.32 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.72 · 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

We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'') dimensional regularization requires only a covariant finite two-loop counterterm. This counterterm is nonvanishing and given by R/8.

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References
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8 arXiv papers cite this in 18 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 · 16 sentences without a confident label

Uses its method or tool 2 papers
  • By dimensionally extending the cubic vertex [equation] the above integral becomes [equation] where $(t,t')=-β^-1⟨q(t) q(t')⟩$ and $_F(t,t') =β^-1⟨χ(t) χ̅(t')⟩$ (the bar indicates Majorana conjugation, see [ref] ) are the dimensionally regulated propagators where $∂ / _F =-_F ∂ / ' = δ^(d+1)(t,t')$, and $_A_B(t,t')=∂_A∂'_B (t,t')$.

    Extended SUSY quantum mechanics: transition amplitudes and path integrals · Dimensional regularization · 0.93

  • The computation of scattering amplitudes of the scalar particle with photons and gravitons, can be performed by considering the worldline representation in curved space [ref] .

    Compton-like scattering of a scalar particle with N photons and one graviton · Insertion of a graviton · 0.87

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