Starting from the Fierz transform of the two-flavour ’t Hooft interaction (a four-fermion Lagrangian with antisymmetric Lorentz tensor interaction terms augmented by an NJL type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we show that: (1) antisymmetric tensor Nambu-Goldstone bosons appear provided that the scalar and tensor couplings stand...

Let G be a countable Abelian group with Zd as a subgroup so that G/Zd is a locally finite group. (An Abelian group is locally finite if every element has finite order.) We can construct a rank one action of G so that the Z-subaction is 2-simple, 2-mixing and only commutes with the other transformations in the action of G. Applications of this construction include a transformation with square ro...

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms toge...

A systematic method is presented for the construction and classification of algebras gauge transformations arbitrary high rank tensor fields. For every field a given rank, transformation will be stated, in generic way, via an ansatz that contains all possible terms, with coefficients maximum number functions. The requirement closure algebra prove to restrictive, but, nevertheless, leave variety...

We call rectangles Gell-Mann matrices rectangle matrices which make generalization of the expression of a tensor commutation matrix n ⊗ n in terms of tensor products of square Gell-Mann matrices.

The exterior square of a multiset is a natural combinatorial construction which is related to the exterior square of a vector space. We consider multisets of elements of an abelian group. Two properties are defined which a multiset may satisfy: recognisability and involution-recognisability. A polynomial-time algorithm is described which takes an input multiset and returns either (a) a multiset...