In the fall of 1994 E. Witten announced a “new gauge theory of 4-manifolds”, capable of giving results analogous to the earlier theory of Donaldson (see [13]), but where the computations involved are “at least a thousand times easier” (Taubes). The new theory begins with the introduction of the monopole equations, whose physical motivation lies in the new results in N = 2 supersymmetric Yang-Mi...

The Schwinger model, defined in the space interval −L ≤ x ≤ L, with (anti)periodic boundary conditions, is canonically quantized in the lightcone gauge A− = 0 by means of equal-time (anti)commutation relations. The transformation diagonalizing the complete Hamiltonian is explicitly constructed, thereby giving spectrum, chiral anomaly and condensate. The structures of Hilbert spaces related both...

We consider the 4d compact U (1) gauge theory with fundamental-adjoint action on a hypertorus. We give a full characterization of the phase diagram of this model in terms of topological flux sectors. 1. The flux in abelian gauge theories Consider an abelian gauge theory defined on a hypercube of size L and periodic boundary conditions. In the continuum the definition of flux through any (µ, ν) ...

By abstracting a connection between gauge symmetry and gauge identity on a noncommutative space, we analyse star (deformed) gauge transformations with usual Leibniz rule as well as undeformed gauge transformations with a twisted Leibniz rule. Explicit structures of the gauge generators in either case are computed. It is shown that, in the former case, the relation mapping the generator with the...

By abstracting a connection between gauge symmetry and gauge identity on a noncommutative space, we analyse star (deformed) gauge transformations with usual Leibnitz rule as well as undeformed gauge transformations with a twisted Leibnitz rule. Explicit structures of the gauge generators in either case are computed. It is shown that, in the former case, the relation mapping the generator with t...

We construct the theory of non-abelian gauge antisymmetric tensor fields, which generalize the standard Yang-MIlls fields and abelian gauge p-forms. The corresponding gauge group acts on the space of inhomogeneous differential forms and it is shown to be a supergroup. We construct the theory of non-abelian gauge antisymmetric tensor fields, which generalize the standard Yang-MIlls fields and ab...