In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are
associated to ordinary knots and links (in 3 dimensions) and to 2-knots (in 4 dimensions) …

This is an introductory review of topological field theories (TFTs) called AKSZ sigma models.
The AKSZ construction is a mathematical formulation for the construction and analysis of a …

The classical action for pure Yang–Mills gauge theory can be formulated as a deformation of
the topological BF theory where, beside the two-form field B, one has to add one extra-field η …

We study four dimensional gauge theories in the context of an equivariant extension of the
Batalin-Vilkovisky (BV) formalism. We discuss the embedding of BV Yang-Mills (YM) theory …

Using the BF version of pure Yang-Mills, it is possible to find a covariant representation of
the't Hooft magnetic flux operator. In this framework,'t Hooft's pioneering work on …

Yang-Mills theory in the first order formalism appears as the deformation of a topological
field theory, the pure BF theory. We discuss this formulation at the quantum level, giving the …

The YM theory has been generalized to 2YM and 3YM theories. Similarly, we generalize the
BFYM theory to “2BFYM” and “3BFYM” theories. Then, we show that these higher BFYM …

We study the differential geometry of principal G-bundles whose base space is the space of
free paths (loops) on a manifold M. In particular we consider connections defined in terms of …

The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type
topological field theory is studied. It is shown that the deformed quantum field theory is …

We present a general approach to construct a class of generalized topological field theories
with constraints by means of generalized differential calculus and its application to …