## Introduction to Quantum Principal Bundles## by Micho Durdevich
Introduction ## IntroductionIn diversity of mathematical concepts and theories a fundamental role is played by those giving a unified treatment of different and at a first sight mutually independent circles of problems.As far as classical differential geometry is concerned, such a fundamental role is given to the theory of principal bundles. Various basic concepts of theoretical physics are also naturally expressible in the language of principal bundles. Classical gauge theory and general relativity theory are paradigmic examples. But classical geometry is just a very special case of a much deeper
So it is natural to ask what would be the analogs of principal bundles
in quantum geometry. And it is reasonable to expect that
such During last years, I have been developing a general theory of quantum principal
bundles, where All my scientific papers mentioned here are available for a direct download (in Tex, PostScript and PDF) from the main download page. Here we shall discuss basic ideas of the theory, trying to speak informally and paying a special attention to interesting purely quantum phenomenas appearing in the game. It is not difficult to incorporate the basic geometrical idea of a principal
bundle, into
the noncommutative context. Let
is commutative. Here
is the coproduct map
Now having the action of Geometrically, the idea is that smooth functions on M are just smooth functions on P
constant along the action orbits.
In such a way, we arrive to [Next Segment]: Differential Caluclus on Quantum Principal Bundles |