Chern-Simons Forms appears in several places in physics for examples,
Fractional Quantum Hall Effect,
response of Topological Insulator,
invariant of knot,
electromagnetism in 2+1 space-time, and so on.
I need to know about:
endomorphism bundle.
endomorphism bundle valued forms.
exterior covariant derivatives of endomorphism bundle valued forms.
trace of endomorphism bundle valued $p$-forms.
wedge product of endomorphism bundle-valued p-forms and endomorphism bundle-valued $q$-forms.
exterior derivative of Chern-Simons form.
exterior covariant derivative of endomorphism bundle-valued $p$-forms.
I am also looking for a book in which required mathematics for working with Chern-Simons forms are discussed. Is there a book in which at least on section was devoted to my questions?
In Knot and Physics by Kauffman, I can not find exterior covariant derivative of endomorphism bundle valued forms, trace of endomorphism bundle valued forms, and so on. This book is about Reidemeister moves, writhe number, and so on.
In Geometry, Topology and Physics by Nakahara Chapter 10, I can only find exterior covariant derivative of bundle-valued p-forms (vertor valued p-form). How can I work with endomorphism bundle valued p-forms?
I have problems with Gauge Fields, Knots, and Gravity by Baez and Mouniani. I think more than 50 present of concepts in this book were left as exercises for reader. Unfortunately all my questions were left as exercises in this book.
In mathematical book like Differential Forms and Connections by Darling, my questions were left as an exercise in p. 210.
