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Rigid Particle and its Spin Revisited
High Energy Physics - Theory · Submitted 30 Dec 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified.
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The abstract, sentence by sentence
The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified. The usual arguments against the inadmissibility of such functions, concerning hermiticity, orthogonality, behavior under rotations, etc., are all shown to be related to the unsuitable choice of functions representing the states with opposite projections of angular momentum. By a correct choice of functions and definition of inner product those difficulties do not occur. And yet the orbital angular momentum in the ordinary configuration space can have integer eigenvalues only, for the reason which have roots in the nature of quantum mechanics in such space. The situation is different in the velocity space of the rigid particle, whose action contains a term with the extrinsic curvature.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified. | contribution 0.84 | 0.64 | 0.21 | asserted 0.98 |
| s1 | The usual arguments against the inadmissibility of such functions, concerning hermiticity, orthogonality, behavior under rotations, etc., are all shown to be related to the unsuitable choice of functions representing the states with opposite projections of angular momentum. | result 0.49 | 0.73 | 0.19 | asserted 1.00 |
| s2 | By a correct choice of functions and definition of inner product those difficulties do not occur. | result 0.73 | 0.62 | 0.22 | asserted 1.00 |
| s3 | And yet the orbital angular momentum in the ordinary configuration space can have integer eigenvalues only, for the reason which have roots in the nature of quantum mechanics in such space. | background 0.42 | 0.26 | 0.17 | asserted 1.00 |
| s4 | The situation is different in the velocity space of the rigid particle, whose action contains a term with the extrinsic curvature. | contribution 0.33 | 0.33 | 0.17 | asserted 1.00 |
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Original abstract
The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified. The usual arguments against the inadmissibility of such functions, concerning hermiticity, orthogonality, behavior under rotations, etc., are all shown to be related to the unsuitable choice of functions representing the states with opposite projections of angular momentum. By a correct choice of functions and definition of inner product those difficulties do not occur. And yet the orbital angular momentum in the ordinary configuration space can have integer eigenvalues only, for the reason which have roots in the nature of quantum mechanics in such space. The situation is different in the velocity space of the rigid particle, whose action contains a term with the extrinsic curvature.
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How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Cites it as background 2 papers
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Not long after that, Plyushchay investigated the $(3+1)$-dimensional model governed by the action $𝒮$ in both cases of $m=0$ and $m≠0$ [ref] .[ This and similar models have also been investigated in, e.g., Refs. [ref] .] He studied the canonical Hamiltonian formalism based on $𝒮$ and the subsequent canonical quantization of the system.
Twistor formulation of a massive particle with rigidity · Introduction · 0.97
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Several types of 4-dimensional models of relativistic point particles with rigidity have been studied until recently from various points of view [ref] .
Spinor and twistor formulations of massless particles with rigidity · Introduction · 1.00
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