(Op)lax natural transformations, twisted quantum field theories, and “even higher” Morita categories

Twisted Conformal Field Theories and Morita equivalence

The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter θ (in appropriate units): an isomorphism is established between an abelian noncommutative field theory (NCFT) and a nonabelian theory of twisted fields on ordinary space. We focus on a particular conformal field theory (CFT), the one obtained by means ...

Twisted Poincaré Invariant Quantum Field Theories

It is by now well known that the Poincaré group acts on the Moyal plane with a twisted coproduct. Poincaré invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincaré action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the...

Natural Transformations. Discrete Categories

We present well known concepts of category theory: natural transofmations and functor categories, and prove propositions related to. Because of the formalization it proved to be convenient to introduce some auxiliary notions, for instance: transformations. We mean by a transformation of a functor F to a functor G, both covariant functors from A to B, a function mapping the objects of A to the m...

Topological Quantum Field Theories on Generalized Cobordism Categories

Invariants of Higher-Dimensional Knots and Topological Quantum Field Theories

The present work can be divided into two main parts: i) the first deals with the functionalintegral quantization via BV formalism of BF theories in any dimension, and ii) the second with (isotopy-) invariants of higher-dimensional knots in Euclidean spaces. We briefly comment on the motivations and the results of part i) and ii). BF theory in 3 dimensions (with the addition of a so-called “cosm...