Poisson structure and Moyal quantisation of the Liouville theory

Jorjadze, George; Weigt, G.

doi:10.1016/s0550-3213(01)00525-9

Cited by 16 publications

(26 citation statements)

References 21 publications

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“…Such a procedure gives an anomaly-free quantum Liouville theory only if additional quantum deformations are taken into consideration [4][5][6][7][8]. A quantum realisation of (11), consistent with the operator Liouville equation and the canonical commutation relations, was so constructed in [6].…”

Section: Vertex Operatorsmentioning

confidence: 99%

“…Nevertheless, its quantum description is still incomplete. By canonical quantisation [4][5][6][7][8] it could be shown that the operator Liouville equation and the Poisson structure of the theory, including the causal non-equal time properties, are consistent with conformal invariance and locality [6,8], but exact results for Liouville correlation functions remained rare [9] despite of ambitious programmes [10,11].…”

Section: Introductionmentioning

confidence: 99%

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Correlation functions and vertex operators of Liouville theory

Jorjadze¹,

Weigt

2004

Physics Letters B

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We calculate correlation functions for vertex operators with negative integer exponentials of a periodic Liouville field, and derive the general case by continuing them as distributions. The path-integral based conjectures of Dorn and Otto prove to be conditionally valid only. We formulate integral representations for the generic vertex operators and indicate structures which are related to the Liouville S-matrix.

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Section: Vertex Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Correlation functions and vertex operators of Liouville theory

Jorjadze¹,

Weigt

2004

Physics Letters B

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“…But much simpler results can arise when the contributions from the different chiralities are pieced together. This was observed recently for non-equal time Poisson brackets of a gauged WZNW theory, namely the Liouville theory [4]. Since WZNW models and their coset theories turn up in many areas of mathematics and physics, it is worthwhile to add the corresponding results for other WZNW theories.…”

mentioning

confidence: 67%

“…In this case only one component of the WZNW field, g 12 (z,z), is gauge invariant, and it is identified with the Liouville exponential [5,4] g 12 (z,z) = e −γϕ(z,z) .…”

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confidence: 99%

Causal Poisson brackets of the WZNW model and its coset theories

Ford

Jorjadze²,

Weigt

2001

Physics Letters B

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From the basic chiral and anti-chiral Poisson bracket algebra of the SL(2, R) WZNW model, non-equal time Poisson brackets are derived. Through Hamiltonian reduction we deduce the corresponding brackets for its coset theories.The analysis of WZNW models is usually reduced to a separate treatment of its chiral or Here we consider the SL(2, R) WZNW model together with its three cosets, the Liouville theory and both the euclidean and Minkowskian black hole models. The general solution of the WZNW equations of motion gives g(τ, σ) as a product of chiral and anti-chiral fields g(z) andḡ(z), where z = τ + σ,z = τ − σ are light cone coordinates.For periodic boundary conditions, the chiral and anti-chiral fields have the monodromiesWe use the following basis of the sl(2, R) algebraIt satisfies the relations t m t n = −η mn I + ǫ mn l t l , where I is the unit matrix, η mn = diag(+, −, −) the metric tensor of 3d Minkowski space, and ǫ 012 = 1. For the matrices t n 1 email: ford@ifh.de 2

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“…To prepare the system for quantization an alternative description in terms of a free field has been given, similar to the corresponding construction for the Liouville field theory on a cylinder [11,12,13,14,15].…”

Section: Discussionmentioning

confidence: 99%

Boundary Liouville Theory: Hamiltonian Description and Quantization

Dorn

Jorjadze²

2007

SIGMA

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Abstract. The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the strip and obeying constant conformally invariant conditions on both boundaries. Depending on the values of the two boundary parameters these solutions may have different monodromy properties and are related to bound or scattering states. By Bohr-Sommerfeld quantization we find the quasiclassical discrete energy spectrum for the bound states in agreement with the corresponding limit of spectral data obtained previously by conformal bootstrap methods in Euclidean space. The full quantum version of the special vertex operator e −ϕ in terms of free field exponentials is constructed in the hyperbolic sector.

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Poisson structure and Moyal quantisation of the Liouville theory

Cited by 16 publications

References 21 publications

Correlation functions and vertex operators of Liouville theory

Correlation functions and vertex operators of Liouville theory

Causal Poisson brackets of the WZNW model and its coset theories

Boundary Liouville Theory: Hamiltonian Description and Quantization

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