Lie algebraic structures in integrable models, affine Toda field theory

This PhD thesis is concerned with integrable quantum field theories in one space and one time dimension. A field theory is said to be 'integrable' if it possesses an infinite set of conservation laws. The latter tremendously restrict the dynamics. For instance, there is no particle production and the individual particle momenta are conserved in a scattering process. Most importantly, the scattering matrix factorizes in two-particle amplitudes. This enables one to construct scattering matrices in an exact and complete manner. Since the S-matrix contains all relevant information about the dynamics this allows for a non-perturbative treatment of these models. The insight gained is expected to be of great value when investigating higher-dimensional quantum field theories. The most prominent class of integrable quantum field theories in 1+1 dimensions is affine Toda field theory. Distinguished by a rich underlying Lie algebraic structure these models have in recent years attracted much attention not only as test laboratories for non-perturbative methods in quantum field theory but also in the context of off-critical models. After a short introduction the mathematical preliminaries such as root systems, Coxeter geometry, dual algebras, q-deformed Coxeter elements and q-deformed Cartan matrices are introduced. Using this mathematical framework the bootstrap analysis of the affine Toda S-matrices with real coupling is performed and several universal Lie algebraic formulae proved. The Lie algebraic methods are then extended to define a new class of colour valued S-matrices and also here universal expressions are derived. The second part of the thesis presents a detailed analysis of the high-energy regime of the integrable models discussed in the first part. By means of the thermodyna mic Bethe ansatz the central charges of the ultraviolet conformal field theories are calculated and in case of affine Toda theories also the first order term in the scaling function is analytically obtained. For the colour valued S-matrices the connection to WZNW coset models is discussed. A particular subclass of them, the so-called Homogeneous Sine-Gordon models, is investigated in some detail and it is found that the presence of unstable particles in these theories gives rise to a staircase pattern in the corresponding scaling function.

Author dc:creator

• Korff, Christian

• integrable quantum field theory
• exact S-matrices
• conformal field theory
• 05.20.Cg
• 05.70.Fh
• 05.10.Ln
• 64.70.Dv

Licence dc:rights.uri

• http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen

Language dc:language

eng

Identifier URI

http://dx.doi.org/10.17169/refubium-5477

OAI record oai:identifier

https://refubium.fu-berlin.de/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Arefubium.fu-berlin.de%3Afub188%2F1275