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Symmetry and Integrability of Non-Singlet Sectors in Matrix Quantum Mechanics
High Energy Physics - Theory · Submitted 10 Jul 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim An interesting feature of the spectrum of these charges in the non-singlet sectors is that they are identical to those of the singlet sector except for the multiplicities.
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The abstract, sentence by sentence
We study the non-singlet sectors of matrix quantum mechanics (MQM) through an operator algebra which generates the spectrum. The algebra is a nonlinear extension of the W_\infty algebra where the nonlinearity comes from the angular part of the matrix which can not be neglected in the non-singlet sector. The algebra contains an infinite set of commuting generators which can be regarded as the conserved currents of MQM. We derive the spectrum and the eigenfunctions of these conserved quantities by a group theoretical method. An interesting feature of the spectrum of these charges in the non-singlet sectors is that they are identical to those of the singlet sector except for the multiplicities. We also derive the explicit form of these commuting charges in terms of the eigenvalues of the matrix and show that the interaction terms which are typical in Calogero-Sutherland system appear. Finally we discuss the bosonization and rewrite the commuting charges in terms of a free boson together with a finite number of extra degrees of freedom for the non-singlet sectors.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the non-singlet sectors of matrix quantum mechanics (MQM) through an operator algebra which generates the spectrum. | contribution 0.99 | 0.95 | 0.09 | asserted 1.00 |
| s1 | The algebra is a nonlinear extension of the W_\infty algebra where the nonlinearity comes from the angular part of the matrix which can not be neglected in the non-singlet sector. | contribution 0.56 | 0.59 | 0.09 | asserted 1.00 |
| s2 | The algebra contains an infinite set of commuting generators which can be regarded as the conserved currents of MQM. | result 0.70 | 0.80 | 0.18 | asserted 0.92 |
| s3 | We derive the spectrum and the eigenfunctions of these conserved quantities by a group theoretical method. | method 0.89 | 0.97 | 0.10 | asserted 1.00 |
| s4 | An interesting feature of the spectrum of these charges in the non-singlet sectors is that they are identical to those of the singlet sector except for the multiplicities. | result 1.00 | 0.88 | 0.32 | asserted 1.00 |
| s5 | We also derive the explicit form of these commuting charges in terms of the eigenvalues of the matrix and show that the interaction terms which are typical in Calogero-Sutherland system appear. | result 0.74 | 0.96 | 0.10 | asserted 1.00 |
| s6 | Finally we discuss the bosonization and rewrite the commuting charges in terms of a free boson together with a finite number of extra degrees of freedom for the non-singlet sectors. | contribution 0.66 | 0.95 | 0.16 | asserted 1.00 |
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Original abstract
We study the non-singlet sectors of matrix quantum mechanics (MQM) through an operator algebra which generates the spectrum. The algebra is a nonlinear extension of the W_\infty algebra where the nonlinearity comes from the angular part of the matrix which can not be neglected in the non-singlet sector. The algebra contains an infinite set of commuting generators which can be regarded as the conserved currents of MQM. We derive the spectrum and the eigenfunctions of these conserved quantities by a group theoretical method. An interesting feature of the spectrum of these charges in the non-singlet sectors is that they are identical to those of the singlet sector except for the multiplicities. We also derive the explicit form of these commuting charges in terms of the eigenvalues of the matrix and show that the interaction terms which are typical in Calogero-Sutherland system appear. Finally we discuss the bosonization and rewrite the commuting charges in terms of a free boson together with a finite number of extra degrees of freedom for the non-singlet sectors.
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