Here, we introduce and apply non-Abelian tensor Berry connections to topological phases in multi-band systems. These gauge behave as antisymmetric fields momentum space naturally generalize Abelian ordinary (vector) connections. We build these novel from momentum-space Higgs fields, which emerge the degenerate band structure of degenerate-band models. Firstly, show that conventional invariants ...

Two one-parameter families of twists providing κ−Minkowski ∗−product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. First one is the Hopf module algebra point of view, which is strictly related with Drinfeld’s twisting tensor technique. An other one relies on an appropriate extension of deformed realizations ...

We consider the secondary fields in D-dimensional space, D ≥ 3, generated by the non-abelian current and energy-momentum tensor. These fields appear in the operator product expansions j a µ (x)ϕ(0) and T µν (x)ϕ(0). The secondary fields underlie the construction proposed herein (see [1,2] for more details) and aimed at the derivation of exact solutions of conformal models in D ≥ 3. In the case ...

‎‎The tensor product is the fundemental ingredient for extending one-dimensional techniques of filtering and compression in signal preprocessing to higher dimensions‎. ‎Woven frames play ‎ a crucial role in signal preprocessing and distributed data processing‎. Motivated by these facts, we have investigated the tensor product of woven frames and presented some of their properties. Besides...

We describe Somekawa’s K-group associated to a finite collection of semi-abelian varieties (or more general sheaves) in terms of the tensor product in Voevodsky’s category of motives. While Somekawa’s definition is based on Weil reciprocity, Voevodsky’s category is based on homotopy invariance. We apply this to explicit descriptions of certain algebraic cycles.

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. The latter play an important role in exposing the duality symmetries of the theory. I this contribution I review recent progress in the construction of action principles for these equations and in particular their non-abelian generalizations.

The complete geometry of quantum states in parameter space is characterized by the geometric tensor, which contains metric and Berry curvature as real imaginary parts, respectively. When are degenerate, take non-Abelian forms. (Abelian) Abelian have been experimentally measured. However, an feasible scheme to extract all components tensor still lacking. Here we propose a generic protocol direct...