Can anyone please suggest some good literature or references for understanding Gauge theory from the perspective of a mathematician (from the point of view of differential geometry)? Being a Mathematics PhD student(differential geometry) I want the introduction mathematically as rigorous as possible.
Specially I want to understand the space of connections and the action of Gauge group on it.
My background is following:
I have read Fibre bundles(principle G-bundles), Theory of Connections( Connection as distribution and as a Lie algebra valued 1-form, Local connection forms, Holonomy Theorem(Ambrose and singer), flat connections and some Affine Connections from Foundation of Differential Geometry(Kobayashi and Nomizu) Vol-1, Characteristic Classes(Chern classes) from Foundation of Differential Geometry(Kobayashi and Nomizu) Vol-2, general theory of fibre bundles(Milnor's classification for principle bundles) from Fibre Bundles Dale Husemoller and I have some idea about basic Algebraic topology, cohomology theory and Category theory(at level of a Masters student in Mathematics).
Most of the literature I came across in the internet I felt they were written from the perspective of a Physicist otherwise some research papers (which I felt too advanced for me now). Being just a 1st year PhD student(differential geometry) it would be really helpful for me if someone can refer (keeping in mind of my Mathematical background) a humble but Mathematically very rigorous literature in Gauge theory where action of Gauge group on the space of Connections is discussed in details.
Thanks in advance.