Relativistic Harmonic Oscillator and Superconvergent Amplitudes

Cocho, G.; Frønsdal, C.; Grodsky, I. T.; White, R. B.

doi:10.1103/physrev.162.1662

Cited by 20 publications

(1 citation statement)

References 11 publications

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“…which 1s G L ( 4, R) invariant, and the deformation operator in addition to (12). Equation (23) is also written as It is now important to note the isomorphism 13 ) S£(4, R)=S0(3, 3).…”

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confidence: 99%

Wave Equation with Mass and Spin Spectrum Based on O(3,3) Group for Relativistic Deformable Model

Takabayasi

1967

Progress of Theoretical Physics

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On the basis of the fact that the group SL(4,R) of relativistic linear deformation and rotation is isomorphic to S0(3,3), new transformation properties under the physical Lorentz transformation is assigned to the internal coordinate in the bilocal-type model, which is adopted as a simple relativistic example having internal movement. The new viewpoint leads to both integer and half-integer spin states and also to the first order wave equation, which contains a mass spectrum corresponding to infinite:dimensional representations of the inner Lorentz group.On the other hand several versions of bilocal model which belong to the conventional identification of inner Lorentz group and represent oscillator or rotator type internal motion are successively discussed in the Appendix. § 1. IntroductionThe relativistic description of a model with internal movement must correspond to representations of the direct product group(1) where porb denotes the orbital Poincare group acting on the "center-of-mass" coordinates x!L alone, and cin is a non-compact group containing as subgroup the inner (homogeneous) Lorentz group Lin whose generators Sp,v are responsible for the spin.*) The physical Lorentz group L LcLorbxLinIs generated by the angular momentum tensor (2) where PM is the translation operator satisfying [Xp,, Pv]

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“…which 1s G L ( 4, R) invariant, and the deformation operator in addition to (12). Equation (23) is also written as It is now important to note the isomorphism 13 ) S£(4, R)=S0(3, 3).…”

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confidence: 99%

Wave Equation with Mass and Spin Spectrum Based on O(3,3) Group for Relativistic Deformable Model

Takabayasi

1967

Progress of Theoretical Physics

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On the Lie Group of Projective Canonical Transformations

Flach

Kirschbaum

1989

Annalen der Physik

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A b s t r a c t . The transformation properties of the projective canonical group are considered. It is shown that the group acts transitiv on functions defined on configuration space but not transitiv on those defined on the phase space. We prove moreover that this group is the largest finite-dimensional Lie group of point transformations determined on the configuration space.ffber die Lie-Gruppe der projektiven kanonischen Transformationen I n h a l t sii bersicht. Die Transformationseigenschaften der projektiven kanonischen Gruppe werden betrachtet. Wir zeigen, dill3 die Gruppe transitiv ist in dem iiber dem Konfigurationsraum definierten Funktionenraum, wahrend sie in dem uber dem Phasenraum definierten Funktionenraum nicht transitiv ist. Es wird aul3erdem bewiesen, daB diese Gruppe die grodte endlich-dimensionale Lie Gruppe in den iiber dem Konfigurtztionsranm definierten Punkttransformat,ionen ist.

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Covariant Harmonic Oscillators and the Quark Model

Kim¹,

Noz²

1988

Special Relativity and Quantum Theory

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Relativistic Harmonic Oscillator and Superconvergent Amplitudes

Cited by 20 publications

References 11 publications

Wave Equation with Mass and Spin Spectrum Based on O(3,3) Group for Relativistic Deformable Model

Wave Equation with Mass and Spin Spectrum Based on O(3,3) Group for Relativistic Deformable Model

On the Lie Group of Projective Canonical Transformations

Covariant Harmonic Oscillators and the Quark Model

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