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Lie Groups and Propagators Exemplified

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T.L. Curtright, Z. Cao, A. Peca, D. Sarker, B.D. Shrestha

Quantum Physics · Submitted 29 Dec 2021

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

The authors' main claim Concise methods are used to compute the propagator for a non-relativistic particle subject to a potential with x^2 and 1/x^2 terms.

how it is stated · asserted 1.00 read the record →

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arXiv ID2112.14401 (version 1)
Pith IDYJ45VB2H, Pith's permanent record of this paper and its review
CitationA. Peca, B.D. Shrestha, D. Sarker, T.L. Curtright, Z. Cao. "Lie Groups and Propagators Exemplified." arXiv:2112.14401 (2021). https://pith.science/paper/YJ45VB2H
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,608 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.05 · mentions code or data availability 0.02.

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

Concise methods are used to compute the propagator for a non-relativistic particle subject to a potential with x^2 and 1/x^2 terms.

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 Concise methods are used to compute the propagator for a non-relativistic particle subject to a potential with x^2 and 1/x^2 terms. contribution 0.66 0.88 0.40 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.52 · evidence from proof or derivation 0.98.

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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

Concise methods are used to compute the propagator for a non-relativistic particle subject to a potential with x^2 and 1/x^2 terms.

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2 arXiv papers cite this in 6 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 · 4 sentences without a confident label

Uses its method or tool 1 paper
  • In order to simulate the quantum Harmonic oscillator Hamiltonian $H=p^2/2m + mω^2x^2/2$ for the case $m=1/2, ω=2$, we use a disentangling formula that expresses the Hamiltonian as a product of three terms, each diagonal in either the standard or the Fourier basis [ref] : exp( -it (p^2 + x^2) ) = exp( - i x^2 tan(t)/2 ) exp( - i p^2 sin(2t) /2 ) exp( - i x^2 tan(t)/2 ) qho The disentangling formula directly yields an extremely efficient quantum circuit for simulating the Hamiltonian $H$.

    Efficient quantum loading of probability distributions through Feynman propagators · Example: the normal distribution and the harmonic oscillator · 1.00

Cites it as background 1 paper
  • The oscillator versus free particle correspondence has been studied subsequently by many people, see [ref] for a (very) incomplete list.

    Gravitational Waves and Conformal Time Transformations · Introduction: gravitational waves and the Niederer transformation · 1.00

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