… This paper presents the formalization of the complete gauge integral theory in HOL4 [8], …
of the gauge integral and present the formalization of the properties and theorems in HOL4. In …

… integral is finite are also gauge integrable. With the monotone convergence of the gauge
integral … measurable functions with a finite integral are gauge integrable. And finally we show …

… Firstly, we extend the existing integration theory of HOL4 by formalizing a … the HOL4 theorem
prover as part of the reported work. Some of the important properties of the Gauge integral, …

… gauge theory partition function can be exactly computed. We consider the N = 2, the N = 2∗
and the N = 4 Yang-Mills theory … Around the trivial background, no fields in the path integral …

… This is of course a procedure standard in gauge theories in general, and in Chern-Simons
theories in particular 17,31, and we will not repeat the details here. See Refs. 19,32 for more …

… path integral over the space of connections (divided by the volume of the gauge group, as
… In the simple two dimensional theory under consideration here, this integral can be defined …

… gauge transformations which lead from one gauge to another. Alternatively, we might try
to formulate the theory in terms of gauge-… "real" quantities in the theory. Thus instead of the …

… We consider the noncommutative field theory widely studied in the context of string theory.
It was shown that the non-vanishing NS-NS B field will induce noncommutative space on the …

… find a path from gauge theory to gravity as directly as possible. Thus let us imagine that we
know a bit about gauge theory and a bit about gravity but nothing about string theory, and ask…