Quantum exchange algebra and locality in Liouville theory

Fujiwara, Takanori; Igarashi, Hiroshi; Takimoto, Yoshio

doi:10.1016/s0370-2693(96)01464-5

Cited by 3 publications

(14 citation statements)

References 20 publications

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“…* Three of the present authors also carried out the analysis within the vector scheme by applying the algebraic method developed in ref. [9] and reconfirmed the operator solution to all order of cosmological constant [11].…”

Section: Introductionmentioning

confidence: 72%

“…In ref. [11] the locality and the canonical commutation relations in Liouville theory were separately discussed and their intimate relationship was not so clarified. This was mainly due to the use of the vector scheme.…”

Section: Canonical Structure Of Classical Toda Field Theorymentioning

confidence: 99%

“…The method is rather restricted to A 2 case and becomes intractable as one goes to higher orders though the basic ideas undelying the arguments presented there could equally well be applied for general Toda systems. The purpose of this paper is to investigate it from a more general setting that is not specialized to a particular Toda system as possible as we can, and to generalize the algebaric method developed for Liouville theory [9,11] to higher rank systems containing more than one screening charges. Since chiral approach is more convenient than vectorial one, we shall show that a chiral structure can be defined for Toda systems written in vector scheme without introducing any extra degrees of freedom, and mostly work in the chiral schematic description.…”

Section: Introductionmentioning

confidence: 99%

“…The generalization of the algebraic method of ref. [11] to A 2 -system is not straightforward due to the fact that the exchange algebra of the screening charges can not be realized by a simple quantum mechanical system as in Liouville theory. We need to truncate the full screening charges to solve the locality constraints so that the algebra of the truncated operators allows a quantum mechanical realization.…”

Section: Introductionmentioning

confidence: 99%

“…4 the exponential operators of A 2 -system are obtained by extending the algebraic approach of ref. [11]. Sect.…”

Section: Introductionmentioning

confidence: 99%

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Quantum exchange algebra and exact operator solution of A2-Toda field theory

et al. 1999

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Locality is analyzed for Toda field theories by noting novel chiral description in the conventional nonchiral formalism. It is shown that the canonicity of the interacting to free field mapping described by the classical solution is automatically guaranteed by the locality. Quantum Toda theories are investigated by applying the method of free field quantization. We give Toda exponential operators associated with fundamental weight vectors as bilinear forms of chiral fields satisfying characteristic quantum exchange algebra. It is shown that the locality leads to nontrivial relations among the R-matrix and the expansion coefficients of the exponential operators. The Toda exponentials are obtained for A 2 -system by extending the algebraic method developed for Liouville theory. The canonical commutation relations and the operatorial field equations are also examined.

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Section: Introductionmentioning

confidence: 72%

Section: Canonical Structure Of Classical Toda Field Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…4 the exponential operators of A 2 -system are obtained by extending the algebraic approach of ref. [11]. Sect.…”

Section: Introductionmentioning

confidence: 99%