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The Proper Time Equation and the Zamolodchikov Metric

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B. Sathiapalan

High Energy Physics - Theory · Submitted 16 Sep 1995

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

The authors' main claim Second, the condition that the two-point function is the Zamolodchikov metric, implies the proper time equation.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-th/9509097 (version 2)
Pith IDJX3D3VKP, Pith's permanent record of this paper and its review
CitationB. Sathiapalan. "The Proper Time Equation and the Zamolodchikov Metric." arXiv:hep-th/9509097 (1995). https://pith.science/paper/JX3D3VKP
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,115 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.77 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The connection between the proper time equation and the Zamolodchikov metric is discussed. The connection is two-fold: First, as already known, the proper time equation is the product of the Zamolodchikov metric and the renormalization group beta function. Second, the condition that the two-point function is the Zamolodchikov metric, implies the proper time equation. We study the massless vector of the open string in detail. In the exactly calculable case of a uniform electromgnetic field strength we recover the Born-Infeld equation. We describe the systematics of the perturbative evaluation of the gauge invariant proper time equation for the massless vector field. The method is valid for non-uniform fields and gives results that are exact to all orders in derivatives. As a non trivial check, we show that in the limit of uniform fields it reproduces the lowest order Born-Infeld equation.

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 connection between the proper time equation and the Zamolodchikov metric is discussed. background 0.60 0.50 0.17 asserted 0.85
s1 The connection is two-fold: First, as already known, the proper time equation is the product of the Zamolodchikov metric and the renormalization group beta function. background 0.87 0.07 0.23 asserted 1.00
s2 Second, the condition that the two-point function is the Zamolodchikov metric, implies the proper time equation. result 0.58 0.37 0.25 asserted 1.00
s3 We study the massless vector of the open string in detail. contribution 1.00 0.86 0.04 asserted 0.88
s4 In the exactly calculable case of a uniform electromgnetic field strength we recover the Born-Infeld equation. result 0.99 0.87 0.12 asserted 1.00
s5 We describe the systematics of the perturbative evaluation of the gauge invariant proper time equation for the massless vector field. method 0.56 0.90 0.09 asserted 0.97
s6 The method is valid for non-uniform fields and gives results that are exact to all orders in derivatives. method 0.47 0.84 0.15 asserted 1.00
s7 As a non trivial check, we show that in the limit of uniform fields it reproduces the lowest order Born-Infeld equation. result 0.96 0.93 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.72 · evidence from proof or derivation 1.00.

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  • figures and tables
  • references and citing sentences
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  • P abstract
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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

The connection between the proper time equation and the Zamolodchikov metric is discussed. The connection is two-fold: First, as already known, the proper time equation is the product of the Zamolodchikov metric and the renormalization group beta function. Second, the condition that the two-point function is the Zamolodchikov metric, implies the proper time equation. We study the massless vector of the open string in detail. In the exactly calculable case of a uniform electromgnetic field strength we recover the Born-Infeld equation. We describe the systematics of the perturbative evaluation of the gauge invariant proper time equation for the massless vector field. The method is valid for non-uniform fields and gives results that are exact to all orders in derivatives. As a non trivial check, we show that in the limit of uniform fields it reproduces the lowest order Born-Infeld equation.

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