Post Made Community Wiki by Ben Webster
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AddedThanks for your answers. Gauge field theory seems to be a very wide field, so I should perhaps mention why I want to learn some basics about gauge field theory beside of very strong intrinsic interest.

I am studying phase-space reduction in the context of deformation quantization of systems with finite degrees of freedom. Now I want to know if it is possible to reinterpret this situation (at least as a toy model) in some way in terms of gauge field theories. So my aim is to learn at least as much of gauge field theory that I can understand if and why such an reinterpretation is possible or how far one can go.

The idea to look for lattice gauge theories was the following quote from the paper by Huebschmann et. al.

"Gauge theory in the Hamiltonian approach, phrased on a finite spatial lattice, leadsto tractable finite-dimensional models for which one can analyze the role of singularitiesexplicitly. Under such circumstances, after a choice of tree gauge has been made, theunreduced classical phase space amounts to the total space $T^* (K \times \dots \times K)$ of the cotangent bundle on a product of finitely many copies of the manifold underlying thestructure group $K$. Gauge transformations are then given by the lift of the action of Kon $K \times \dots \times K$ by diagonal conjugation. This leads to a finite-dimensional Hamiltonian system with symmetries."

Why a asked for a "geometric language" is clear because the strength of deformation quantization is in fact in the area of the quantization of systems with a more complex phase-space geometry.

Having this additional information it is perhaps easier for you to give me some hints where to start in literature.

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# Literature for gauge field theory on the lattice in geometrical formulation

I have found an article by Huebschmann, Rudolph and Schmidt: http://www.springerlink.com/content/b8v216v0m8h16264/ about "A Gauge Model for Quantum Mechanics on a Stratified Space" and I am very interested in this subject, but I don't have any background in gauge-field theory or something like that.

So my question is, if there are any good introductory books or overview articles which cover Hamiltonian (quantum) gauge field theory on the lattice in a geometrical mathematical language like the article mentioned above? Especially I am interested in references which deal with more regular cases rather than the singular cases discussed in the article above. Finally it is important that it covers this topic in a way that one can gain a bit deeper physical understanding (without giving up a clear, rigorous and geometrical mathematical language).