I have found an article by Huebschmann, Rudolph and Schmidt 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).
Added
Thanks 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, leads
to tractable finite-dimensional models for which one can analyze the role of singularities
explicitly. Under such circumstances, after a choice of tree gauge has been made, the
unreduced classical phase space amounts to the total space $\mathrm{T}^* (K \times \dots \times K)$ of the cotangent bundle on a product of finitely many copies of the manifold underlying the
structure group $K$. Gauge transformations are then given by the lift of the action of $K$
on $K \times \dots \times K$ 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.
Best Answer
Although not mathematical per se, I personally like Kogut's works for Hamiltonian lattice gauge theory: there is an old RMP article and a rather good book which I purchased specifically for its presentation of the Hamiltonian theory. Of course Kogut introduced the subject along with Wilson in a PRD article, so his presentation of the material is not particularly exotic.
I will say that the advantage of the lattice is that rigor is not really much of an issue unless one wishes to take a continuous limit. Even so the incorporation of material on the Ising theory is helpful in this regard.