Public defence, Mathematics and Statistics, MSc Joonas Vättö

Title of the thesis: Bosonic conformal field theory in the operator formalism

Thesis defender: Joonas Vättö 
Opponent: Professor Ellen Powell, University of Durham, United Kingdom
Custos: Professor Kalle Kytölä, Aalto University School of Science

Quantum field theory stands as the most empirically successful framework for fundamental particle interactions. Though a phenomenological triumph, its mathematical foundations remain an enduring puzzle. Two flavours of challenges arise: where axiomatic field theory concerns itself with the formulation of suitable definitions, constructive field theory aims to demonstrate satisfaction of prescribed axioms in  physically relevant models.

Conformal field theories form a subclass of quantum field theories of particular physical relevance and structural richness. Physicists have known since the 1980s that they describe macroscopic properties of statistical mechanics models at criticality. Despite their importance, no fully satisfactory mathematical framework for conformal field theories currently exists.

This thesis advances the constructive programme for two-dimensional conformal field theory. Field theories of the massless free boson are constructed in the operator formalism via two complementary routes: as transfer matrices of discrete models, and as evolution operators built from a quantisation of classical mechanics models in the continuum. Together, these constructions demonstrate the suitability of the operator formalism as a rigorous framework for constructive conformal field theory.

Key words: mathematical physics, quantum field theory, conformal field theory

Thesis available for public display 7 days prior to the defence at Aalto University's public display page.