  Much of arithmetic geometry is concerned with the study of principal bundles.
They occur prominently in the arithmetic of elliptic curves and, more recently,
in the study of the Diophantine geometry of curves of higher genus. In
particular, the geometry of moduli spaces of principal bundles appears to be
closely related to an effective version of Faltings's theorem on finiteness of
rational points on curves of genus at least 2. The study of arithmetic
principal bundles includes the study of {\em Galois representations}, the
structures linking motives to automorphic forms according to the Langlands
programme. In this article, we give a brief introduction to the arithmetic
geometry of principal bundles with emphasis on some elementary analogies
between arithmetic moduli spaces and the constructions of quantum field theory.
For the most part, it can be read as an attempt to explain standard
constructions of arithmetic geometry using the language of physics, albeit
employed in an amateurish and ad hoc manner.
