Factorized scattering theories in 1+1 dimensions

This thesis investigates whether S-matrices in 1+1 dimensional integrable quantum field theories remain valid at all energy scales or whether their thermodynamic behavior inevitably develops Hagedorn-like singularities that signal a scale where a breakdown of the S-matrix description occurs. We begin with a review of scattering theory and the role of integrability, emphasizing local conserved charges, factorizability, and the Yang–Baxter equation as central consistency conditions. Exact two-particle S-matrices are then constructed via the bootstrap program, providing the framework for analyzing both scattering amplitudes and thermodynamic behavior. We paid close attention to the statistics of the particle spectrum in these integrable models, as the growth and distribution of states directly influence high-energy thermodynamics. Several examples are examined in detail. The examples include the sine-Gordon model as a standard example, the sausage model as a more intricate example, and higher-spin particle theories where a generalized S-matrix construction is developed through the quantum group symmetry algebra U_q({su}_2). The spin 3/2 case is worked out explicitly. These examples allow for a systematic exploration of the validity of the S-matrix framework. The analysis shows that while integrability permits exact control of scattering processes, the thermodynamic properties of certain models suggest potential limitations of the S-matrix description at extreme energies. These findings clarify the domain of validity of S-matrix theories and highlight the role of particle spectrum's statistics in determining whether such theories remain consistent or exhibit signs of Hagedorn-like behavior.