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.


Some classic references (maybe it has been written something better since their publication I don't know) :

  • about Instantons over 4D manifolds, Donaldson & Kronheimer's "The Geometry of four manifold" and Uhlenbeck & Freed's "Instantons and four manifolds"

  • about Seiberg-Witten, J.W. Morgan's "The Seiberg-Witten Equations And Applications To The Topology Of Smooth Four-Manifolds"


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