| Summary: | The mathematical foundations of gauge theory has been studied. The
aspects that has been explained is fiber bundle, connection, and curvature. The
fiber bundle formalism used generalization of manifold that has been endowed
with calculus structure on it. The principal fiber bundle as one of the fiber
bundle is the representation of gauge theory. In principal fiber bundle, connection
is built as distribution of horizontal tangent vector. After that, connection
is interpreted as Lie algebra-valued 1-form on principal fiber bundle to get the
local picture of connection in base manifold. Later on, the concept of horizontal
curve on principal fiber bundle is built to define parallel transport. By using
parallel transport, it can be defined the covariant derivative of principal fiber
bundle�s section. The covariant derivative then generalized to exterior covariant
derivative in principal fiber bundle and use to defined curvature as the Lie
algebra-valued 2-form.
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