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Sum-Over-Histories Quantization of Relativistic Particle

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Pavel Krtous

General Relativity and Quantum Cosmology · Submitted 22 Nov 2000

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

The authors' main claim These terms induce proper boundary conditions for the propagator.

how it is stated · asserted 0.99 read the record →

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arXiv IDgr-qc/0011077 (version 1)
Pith IDIJXC76UP, Pith's permanent record of this paper and its review
CitationPavel Krtous. "Sum-Over-Histories Quantization of Relativistic Particle." arXiv:gr-qc/0011077 (2000). https://pith.science/paper/IJXC76UP
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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, 5,982 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.11 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Sum-over-histories quantization of particle-like theory in curved space is discussed. It is reviewed that the propagator satisfies the Schrodinger equation respective wave equation with a Laplace-like operator. The exact dependence of the operator on the choice of measure is shown. Next, modifications needed for a manifold with a boundary are introduced, and the exact form of the equation for the propagator is derived. It is shown that the Laplace-like operator contains some distributional terms localized on the boundary. These terms induce proper boundary conditions for the propagator. This choice of boundary conditions is explained as a consequence of a measurement of particles on the boundary. The interaction with sources inside of the domain and sources on the boundary is also 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 Sum-over-histories quantization of particle-like theory in curved space is discussed. background 0.54 0.39 0.06 asserted 0.84
s1 It is reviewed that the propagator satisfies the Schrodinger equation respective wave equation with a Laplace-like operator. background 0.86 0.15 0.10 asserted 0.98
s2 The exact dependence of the operator on the choice of measure is shown. result 0.86 0.78 0.12 asserted 1.00
s3 Next, modifications needed for a manifold with a boundary are introduced, and the exact form of the equation for the propagator is derived. contribution 0.78 0.86 0.12 asserted 0.99
s4 It is shown that the Laplace-like operator contains some distributional terms localized on the boundary. result 1.00 0.84 0.21 asserted 1.00
s5 These terms induce proper boundary conditions for the propagator. result 0.88 0.73 0.26 asserted 0.99
s6 This choice of boundary conditions is explained as a consequence of a measurement of particles on the boundary. interpretation 1.00 0.64 0.18 asserted 0.99
s7 The interaction with sources inside of the domain and sources on the boundary is also discussed. contribution 0.97 0.65 0.06 asserted 0.81

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

Sum-over-histories quantization of particle-like theory in curved space is discussed. It is reviewed that the propagator satisfies the Schrodinger equation respective wave equation with a Laplace-like operator. The exact dependence of the operator on the choice of measure is shown. Next, modifications needed for a manifold with a boundary are introduced, and the exact form of the equation for the propagator is derived. It is shown that the Laplace-like operator contains some distributional terms localized on the boundary. These terms induce proper boundary conditions for the propagator. This choice of boundary conditions is explained as a consequence of a measurement of particles on the boundary. The interaction with sources inside of the domain and sources on the boundary is also discussed.

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