Cartan forms and structure equations

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Cartan forms and structure equations are essential for defining differentiation on geometrical objects like fibre bundles, which are crucial in advanced physics, particularly in general relativity and string theory. These concepts help in understanding complex mathematical frameworks that underpin various physical models. The complexity of these topics is significant, often requiring extensive literature for thorough comprehension. For deeper insights, resources like "Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems" by Tom Ivey are recommended. Understanding these concepts is vital for anyone delving into gauge theory and related fields.
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Could someone explain these two concepts? What I need is the big picture of 'why' we need this, roughly 'what' these equations mean, 'where' its used etc
Thanks in advance
 
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omg.. nobody answering...
there aren't many people who understand these stuff eh?:rolleyes:
 
precondition said:
omg.. nobody answering...
there aren't many people who understand these stuff eh?:rolleyes:

i think it is more of a matter of complexity. there are entire books written to answer that question.

I'll give the why, you can explore the what on your own: Cartan forms and connections allow us to define differentiation on certain geometrical objects, namely fibre bundles. This topic has proven valuable in constructing models for phenomena in GR and string theory.

Any book on gauge theory and physics will discuss this. for a heavy duty mathematical treatment, look for the book Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems by my friend Tom Ivey.
 

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