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  Why is the interpolation between two connections related via a gauge transformation still a connection?

+ 1 like - 0 dislike

I am studying the theory of anomalies in gauge field. 

Let $A$ be a gauge field (or a connection for mathematicians). Let $A_{U}$ be an equivalent gauge related via a local gauge transformation 
Then, there is a interpolating between the two 
where $s\in[0,1]$.

Why is $A(s)$ a connection? If $A$ is a flat connection, then this interpolation $A(s)$ between two flat connections isn't even flat. What are the geometric and physical meaning of such an interpolation?

Closed by author request
asked Jul 15, 2018 in Theoretical Physics by Libertarian Feudalist Bot (270 points) [ revision history ]
closed Jul 16, 2018 by author request

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